(PLS HELP, I WILL MARK BRAINLIEST) what is a very easy way to multiply mixed fractions.

Answer:

It should go exponents, multiplication and division, then addition and subtraction

Step-by-step explanation:

By using PEMDAS, for order of operations, it's easier to remember which set comes first. (parentheses, exponents, multiplication, division, addition, subtraction)

Answer:

(a) The expected value of the prize for one play of Instant Lotto is $3.50.

(b) The probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c) The probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

Step-by-step explanation:

(a)

The probability distribution of the monetary prizes that can be won at the game called Instant Lotto is:

X         P (X = x)

$10        0.05

$15        0.04

$30       0.03

$50       0.01

$1000   0.001

$0         0.869

___________

Total =   1.000

Compute the expected value of the prize for one play of Instant Lotto as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=(10\times 0.05)+(15\times 0.04)+(30\times 0.03) \\+ (50\times 0.01)+(1000\times 0.001)+(0\times 0.869)\\=0.5+0.6+0.9+0.5+1+0\\=3.5[/tex]          

Thus, the expected value of the prize for one play of Instant Lotto is $3.50.

(b)

Let X = number of times a visitor wins some prize.

A visitor to the casino is given n = 20 free plays of Instant Lotto.

The probability that a visitor wins at any of the 20 free plays is, p = 1/20 = 0.05.

The event of a visitor winning at a random free play is independent of the others.

The random variable X follows Binomial distribution with parameters n = 20 and p = 0.05.

Compute the probability that the visitor wins some prize at least twice in the 20 free plays as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              [tex]=1-[{20\choose 0}0.05^{0}(1-0.05)^{20-0}]-[{20\choose 1}0.05^{1}(1-0.05)^{20-1}]\\=1-0.3585-0.3774\\=0.2641[/tex]

Thus, the probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c)

Let X = number of people who play Instant Lotto each day.

The random variable X is normally distributed with a mean, μ = 800 people and a standard deviation, μ = 310 people.

Compute the probability that a randomly selected day has at least 1000 people play Instant Lotto as follows:

Apply continuity correction:

P (X ≥ 1000) = P (X > 1000 + 0.50)

                    = P (X > 1000.50)

                    [tex]=P(\frac{X-\mu}{\sigma}>\frac{1000.50-800}{310})[/tex]

                    [tex]=P(Z>0.65)\\=1-P(Z<0.65)\\=1-0.74215\\=0.25785\\\approx0.2579[/tex]

Thus, the probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

The number in question is found by setting up the equation (x + 13) / -7 = -4, and solving for 'x'. Following order of operations and sign rules, we determine that the number is 15.

The question asks us to find a number when given that the quotient of that number increased by 13 and -7 is -4. To solve this, we set up an equation and follow the multiplication and division rules for signs and the order of operations.

Let the unknown number be 'x'. According to the problem, (x + 13) / -7 = -4. Multiplying both sides by -7 to eliminate the denominator, we get x + 13 = (-7)(-4). Applying the rule that the product of two negative numbers is positive, we simplify the right side to get x + 13 = 28. Now, we subtract 13 from both sides to isolate 'x': x = 28 - 13, which gives us x = 15.

The number in question is therefore 15.

Answer:

A

Step-by-step explanation:

If you plug in the numbers to the formula, A is the correct answer.

Answer:

a) - The population consists of all of Danielle's colleagues that could have been one of the randomly surveyed 50.

- The sample is Danielle's 50 colleagues that she ramdomly sampled.

b) From the statistical test performed, there is significant evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) Check Explanation

Step-by-step explanation:

The full complete, correct question is attached to the solution of this question.

a) The population is normally the extended distribution where every selected random sample is extracted from. So, for this question, the population will be all of Danielle's colleagues.

The sample is the subset distribution obtained from the population. In the question, it is stated explicitly that Danielle randomly picked 50 of her colleagues to participate in the survey. Hence, the sample is Danielle's 50 colleagues that she ramdomly sampled.

b) The appropriate statistical inference for this question is to carry out the t-test hypothesis test.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, Danielle wants to prove that she is overpaying for her auto insurance compared to her colleagues.

So, the null hypothesis is that there is no significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

That is, Danielle isn't overpaying for her auto insurance compared to her colleagues or better stated that her colleagues are paying more than or just about the same for auto insurance compared to her.

While, the alternative hypothesis is that there is significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

Let μ be the mean Danielle's colleagues' auto insurance fees.

Mathematically,

The null hypothesis is represented as

H₀: μ ≥ 476

The alternative hypothesis is given as

Hₐ: μ < 476

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = $447

μ₀ = Danielle's auto insurance bill that we're comparing the sample against = $476

σₓ = standard error = [σ/√n]

σ = Sample standard deviation = $75

n = Sample size = 30 (30 colleagues got back to Danielle)

σₓ = [75/√30] = $13.693

t = (447 - 476) ÷ 13.693

t = -2.117 = -2.12

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 30 - 1 = 29

Significance level = 0.05 (Most hypothesis tests are carried out at this level of significance)

The hypothesis test uses a one-tailed condition because we're testing only in one direction. (Checking whether Danielle is overpaying or that the mean is of her colleagues' auto insurance fees is less than Danielle's)

p-value (for t = -2.12, at 0.05 significance level, df = 29, with a one tailed condition) = 0.021342

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.021342

0.021342 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) The two type of errors associated with this test include the Type I and Type II errors.

In Hypothesis testing, A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.

A type II error involves failing to reject the null hypothesis when in reality it should have been rejected. It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.

For this question, a type I error entails obtaining from the statistical test that Danielle is overpaying when she isn't overpaying for her auto insurance compared to her colleagues in reality.

A type II error would be obtaining from the statistical test that Danielle isn't overpaying when she is truly overpaying for her auto insurance compared to her colleagues, in reality.

Hope this Helps!!!

Answer:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Step-by-step explanation:

We define X the random variable that represent the heights of a population for ten year old children, and for this case we know the distribution for X is given by:

[tex]X \sim N(55.7,5.2)[/tex]  

Where [tex]\mu=55.7[/tex] and [tex]\sigma=5.2[/tex]

We want to find this probability:

[tex]P(49.5<X<67.2)[/tex]

We can use the z score formula to solve this problem given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we have:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

And we can find this probability with this difference

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

We can use tables for the normal standard distribution, excel or a calculator and we got this

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.

Step-by-step explanation:

The given is,

                 After six years she withdraws her total balance of $500

                 Interest rate 6 % a year ( compounded )

Step:1

          Formula to calculate the future amount with an compound interest rate,

                                      [tex]F=P(1+r)^{t}[/tex].............................(1)

        Where, F - Future worth amount

                     P - Initial investment

                      r - Rate of interest

                      t - No. of years

Step:2

        From the given,

                   F = $500

                   r = 6%

                   t = 6 years

       Equation (1) becomes,

                           [tex]500 = P(1+0.06)^{6}[/tex]

                                  = [tex]P(1.06)^{6}[/tex]

                                  = P (1.41852)

                              [tex]P= \frac{500}{1.41852}[/tex]

                                  = 352.48

                                  ≅ 353

                              P = $353

Result:

         Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.

Answer:

C- $352.48

Step-by-step explanation:

Just took test :]

Answer:

4/6 > 3/10

Step-by-step explanation:

4/6 < 3/10

First get a common denominator of 30

4/6 *5/5   < 3/10 *3/3

20/30 < 9/30

This is false since 20 > 9

Answer:

The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to build the confidence interval.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95([tex]t_{95}[/tex]). So we have T = 1.7056

The margin of error is:

M = T*s = 1.7056*21.4 = 36.50.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 76.2 - 36.5 = 39.7

The upper end of the interval is the sample mean added to M. So it is 76.2 + 36.5 = 112.7

The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7

X + 3 < 9

Subtract 3 from both sides:

X < 6

The answer is x < 6

Answer:

4 y x '  −  9 x y  −  7 y r '  +  4 x y?  +  12

Step-by-step explanation:

Simplified the expression.

<3

Answer:

4 y x ' − 9 x y − 7 y r ' + 4 x y ? + 12

Answer:

2 1/2 cups

Step-by-step explanation:

You are doubling your recipe. You would do 1 1/4 × 2. First, 1 × 2 = 2 and then 1/4 × 2 = 1/2. Put them together for your answer. I hope this helped.

Final answer:

Parker will need 2 1/2 cups of dip.

Explanation:

To find out how many cups of dip Parker will need, we can set up a proportion using the given information.

The snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies.

Let's call the number of cups of dip Parker needs x.

The proportion will be: 1 1/4 cups / 1/2 cups = x cups / 1 cup.

To solve for x, we can cross multiply and then divide: (1 1/4) * 1 = (1/2) * x.

Simplifying both sides gives us 5/4 = 1/2 * x.

To isolate x, we can multiply both sides by the reciprocal of 1/2, which is 2/1: (5/4) * (2/1) = x.

Multiplying gives us x = 10/4, which simplifies to x = 2 1/2 cups.

Answer:

a =8

Step-by-step explanation:

-5(a + 3) = -55

Distribute

-5a -15 = -55

Add 15 to each side

-5a-15+15 = -55+15

-5a = -40

Divide each side by -5

-5a/-5 = -40/-5

a = 8

Final answer:

To factor a composite number into primes, divide it by its smallest divisor that is not 1, then continue dividing the quotient until all factors are prime. An example is the number 60, which factors into 2 x 2 x 3 x 5, or 2² x 3 x 5 when using exponents for the repeated factor of 2.

Explanation:

The subject of the question is to select a composite number and break down its factors until all the factors are prime. As an example, let's choose the composite number 60. Here's how you can factor it into primes:

First, note that 60 is an even number, so it is divisible by 2. Start by dividing 60 by 2 to get 30.

Now, 30 is still even, so we can divide by 2 again to get 15.

15 is divisible by 3, so when we divide it by 3, we get 5, which is a prime number.

So, the prime factorization of 60 is 2 x 2 x 3 x 5, often written using exponents for any repeated factors as 22 x 3 x 5.

Through factorization, we have converted the composite number into a product of prime factors. Each factor multiplication is a step that requires one to find two numbers that multiply to the number we are factoring and continuing this process until we reach numbers that are prime.

Answer:

  a = 1

Step-by-step explanation:

The problem is written as a linear equation:

  ((1/8)^-3)a = 512

  512a = 512 . . . . simplify

  a = 1 . . . . . . . . . divide by the coefficient of a

___

We suspect you might intend the exponential equation:

  (1/8)^(-3a) = 512

  512^a = 512 . . . . . simplify

  a = 1 . . . . . . . . . . . compare bases and exponents

equivalently, take the log to the base 512:

  a·1 = 1

  a = 1

Answer:

m=log 100s/S

Step-by-step explanation:

howdy!

answer is in the attachment below :)

Answer:

Step-by-step explanation:

Hello!

To test if calcium reduces the symptoms of PMS two independent groups of individuals are compared, the first group, control, is treated with the placebo, and the second group is treated with calcium.

The parameter to be estimated is the difference between the mean symptom scores of the placebo and calcium groups, symbolically: μ₁ - μ₂

There is no information about the distribution of both populations X₁~? and X₂~? but since both samples are big enough, n₁= 228 and n₂= 212, you can apply the central limit theorem and approximate the sampling distribution to normal X[bar]₁≈N(μ₁;δ₁²/n) and X[bar]₂≈N(μ₂;δ₂²/n)

The formula for the CI is:

[(X[bar]₁-X[bar]₂) ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} }[/tex]]

95% confidence level [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53

X₁: Mood swings score of a participant of the placebo group.

X₂: Mood swings score of a participant of the calcium group.

[(0.70-0.50) ± 1.96 * [tex]\sqrt{\frac{0.78^2}{228} +\frac{0.53^2}{212} }[/tex]]

[0.076; 0.324]

(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40

X₁: Crying spells score of a participant of the placebo group.

X₂: Crying spells score of a participant of the calcium group.

[(0.39-0.21) ± 1.96 * [tex]\sqrt{\frac{0.57^2}{228} +\frac{0.40^2}{212} }[/tex]]

[0.088; 0.272]

(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45

X₁: Aches and pains score of a participant of the placebo group.

X₂: Aches and pains score of a participant of the calcium group.

[(0.45-0.37) ± 1.96 * [tex]\sqrt{\frac{0.60^2}{228} +\frac{0.45^2}{212} }[/tex]]

[-0.019; 0.179]

(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61

X₁: Craving for sweets or salts score of a participant of the placebo group.

X₂: Craving for sweets or salts score of a participant of the calcium group.

[(0.60-0.44) ± 1.96 * [tex]\sqrt{\frac{0.75^2}{228} +\frac{0.61^2}{212} }[/tex]]

[0.032; 0.287]

I hope this helps!

Using the z-distribution, the 95% confidence intervals are:

a) (0.08, 0.32).

b) (0.09, 0.27).

c) (-0.02, 0.18).

d) (0.03, 0.29).

We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.

In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.

Item a:

The standard errors are:

[tex]s_P = \frac{0.78}{\sqrt{228}} = 0.0517[/tex]

[tex]s_C = \frac{0.53}{\sqrt{212}} = 0.0364[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.7 - 0.5 = 0.2[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0517^2 + 0.0364^2} = 0.0632[/tex]

The interval is:

[tex]\overline{x} \pm zs[/tex]

Hence:

[tex]\overline{x} - zs = 0.2 - 1.96(0.0632) = 0.08[/tex]

[tex]\overline{x} + zs = 0.2 + 1.96(0.0632) = 0.32[/tex]

The interval is (0.08, 0.32).

Item b:

The standard errors are:

[tex]s_P = \frac{0.57}{\sqrt{228}} = 0.03775[/tex]

[tex]s_C = \frac{0.4}{\sqrt{212}} = 0.02747[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.39 - 0.21 = 0.18[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.03775^2 + 0.02747^2} = 0.0467[/tex]

Hence:

[tex]\overline{x} - zs = 0.18 - 1.96(0.0467) = 0.09[/tex]

[tex]\overline{x} + zs = 0.18 + 1.96(0.0467) = 0.27[/tex]

The interval is (0.09, 0.27).

Item c:

The standard errors are:

[tex]s_P = \frac{0.6}{\sqrt{228}} = 0.0397[/tex]

[tex]s_C = \frac{0.45}{\sqrt{212}} = 0.0309[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.45 - 0.37 = 0.08[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0397^2 + 0.0309^2} = 0.0503[/tex]

Hence:

[tex]\overline{x} - zs = 0.08 - 1.96(0.0503) = -0.02[/tex]

[tex]\overline{x} + zs = 0.08 + 1.96(0.0503) = 0.18[/tex]

The interval is (-0.02, 0.18).

Item d:

The standard errors are:

[tex]s_P = \frac{0.75}{\sqrt{228}} = 0.0497[/tex]

[tex]s_C = \frac{0.61}{\sqrt{212}} = 0.0419[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.60 - 0.44 = 0.16[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0497^2 + 0.0419^2} = 0.065[/tex]

Hence:

[tex]\overline{x} - zs = 0.16 - 1.96(0.065) = 0.03[/tex]

[tex]\overline{x} + zs = 0.16 + 1.96(0.065) = 0.29[/tex]

The interval is (0.03, 0.29).

A similar problem is given at https://brainly.com/question/15297663

Answer:

  17 points

Step-by-step explanation:

20% × 85 = 0.20 × 85 = 17

Jayla scored 17 points.

Answer:360 miles per minute , and 1080 in 3 minutes

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Since they have the same denominator, you can just subtract the numerators. So, 8-2=6.

6/12 can be simplified to 1/2.

Answer:

the answer is 1/2 or 0.5

Step-by-step explanation:

hope this helps!

The total cost of two packets of fig rolls, with the second one at half price, is £1.62. The calculation involves the normal price of one packet plus half of that price for the second one.

The question involves calculating the total cost of fig rolls when a shop offers a deal where if you buy one packet, you get the second packet at half the price.

To find the total cost of two packets under this offer, we first take the normal price of one packet (£1.08) and add it to half of that price (which is £1.08 / 2 = £0.54). The total cost for two packets is therefore £1.08 (first packet) + £0.54 (second packet at half price), which equals £1.62.

For 3 packets of fig rolls and 6 packets of crisps, the total price is £8.42 considering the offers of buy one, get 2nd half price and three for the price of two, respectively.

For the fig rolls:

Normal price for 1 packet = £1.08

Buy one, get 2nd half price.

So, for 3 packets of fig rolls, we'd pay for 2 and get the third at half price.

Total cost for 3 packets of fig rolls = Cost of 2 packets + Half price of 1 packet

[tex]= 2 \times £1.08 + \frac{1}{2} \times £1.08[/tex]

= £2.16 + £0.54

= £2.70

For the crisps:

Normal price for 1 packet = £1.43

Three for the price of two.

So, for 6 packets of crisps, we'd pay for 4 and get 2 free.

Total cost for 6 packets of crisps = Cost of 4 packets

[tex]\(= 4 \times £ 1.43\)[/tex]

= £5.72

Therefore, the total price for 3 packets of fig rolls and 6 packets of crisps would be:

Total = Cost of 3 fig roll packets + Cost of 6 crisps packets

= £2.70 + £5.72

= £8.42

Complete Question:

Answer: The final answer in proper fraction is 169/9

Step-by-step explanation:

Given the expression

-6 4/9-3 2/9-82/9

Firstly let us convert all mixed fraction to proper fraction to further simplify the expression

-58/9 - 29/9 - 82/9

We now have all terms in proper fraction, we can continue by finding the LCM which is 9

= (- 58-29-82)/9

= 169/9

Answer:

Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]

Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)

Now we need to find the degrees of freedom given by:

[tex] df = n_A + n_B -2= 13+10-2=21[/tex]

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

[tex] t_{cric}= 1.721[/tex]

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

Step-by-step explanation:

Data given and notation

[tex]\bar X_{A}=12[/tex] represent the mean for 1

[tex]\bar X_{B}=9[/tex] represent the mean for 2

[tex]s_{A}=5[/tex] represent the sample standard deviation for 1

[tex]s_{2}=3[/tex] represent the sample standard deviation for 2

[tex]n_{1}=13[/tex] sample size for the group 1

[tex]n_{2}=10[/tex] sample size for the group 2

t would represent the statistic (variable of interest)

[tex]\alpha=0.05[/tex] significance level provided

Develop the null and alternative hypotheses for this study

We need to conduct a hypothesis in order to check if the mean for group A is higher than the mean for B:

Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]

Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)

Now we need to find the degrees of freedom given by:

[tex] df = n_A + n_B -2= 13+10-2=21[/tex]

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

[tex] t_{cric}= 1.721[/tex]

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

Question: The question is incomplete. What need to be calculated is not included in the question. Below is the question requirement and the answer.

a) Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object?

Answer:

Mean = 50 minutes

Variance = 725 minutes

Step-by-step explanation:

X₁ = 50

X₂ = 60

X₃ = 40

σ₁ = 15

σ₂ = 20

σ₃ = 10

Calculating the mean E(Y) using the formula;

E(Y) = E(X₁ +X₂ +X₃)/3

        = (EX₁ + EX₂ + EX₃)/3

        = (50 + 60 + 40)/3

       = 50 minutes

Therefore, the mean of the total repair time for this object is 50 minutes

Calculating the variance V(Y) using the formula;

V(Y) = V(X₁ +X₂ +X₃)

       = E(X₁) +E(X₂) + E(X₃)

       = σ₁² + σ₂² + σ₃²

        = 15² + 20² + 10²

        = 225 + 400 + 100

         = 725 minutes

Therefore, the variance of the total repair time for this object is 725 minutes

Answer:

p=population of Floridians that would support the amendment

Step-by-step explanation:

we are given parameters are,

n = Sample size = 500

and p = Population proportion = 60% = 0.6  

p = the population proportion of Floridians that would the amendment.

Answer:

A

Step-by-step explanation:

The complete question is:

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment. A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. Define the parameter.

A) phat= sample proportion of 500 Floridans that would support the ammendment

B) p= population proportion of Floridans that would support the ammendment

C) phat= population proportion of Floridans that would support the ammendment

D) p= sample proportion of 500 Floridans that would support the ammendment

p is the actual probability of an event which is 0.6

phat is the value calculated from the sample observation

here a sample of 500 Floridans is taken and probability from sample is being observed.  So phat is the parameter which is the population proportion of 500 Floridans that would support the ammendment

Answer:

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Step-by-step explanation:

The success probability is p = 70% = 0.70

The number of trials are n = 25

The Excel formula for the binomial distribution is given by

BINOMDIST(Number_s, Trial_s, Probability_s, Cumulative)

Where

Numbers = 5 and 10

Trials = 25

Probability = 70%

Cumulative = FALSE

The probability of between 5 and 10 customers is then

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Note: FALSE option provides the probability of exactly 10 and 5 where TRUE option gives cumulative results (0 to 5 or 0 to 10) that would be wrong in this case.

Using the binomial distribution, it is found that the Excel statement that will find the probability of between 5 and 10 customers is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For each customer, there are only two possible outcomes, either they purchase a pair of running shoes, or they do not. Customers' purchases are independent, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Using Excel, the probability of the number of successes being between a and b, inclusive, is given by:

BINOM.DIST.RANGE(n, p, a, b)

In this problem:

Then, the Excel statement is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For more on the binomial distribution, you can check https://brainly.com/question/24863377

Answer:

(D) 180 degrees

Step-by-step explanation:

There are 12 hours on the clock.

For each 1 hour, the hour hand rotates = [tex]360^0 \div 12=30^0[/tex]

From 8 o'clock in the morning to 2 o'clock in the afternoon= 6 Hours

Therefore:

Number of degrees rotated by the hour hand = [tex]6 X 30^0 =180^0[/tex]

The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 12/95.

The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is the product of the probability of choosing a purple jelly bean and the probability of choosing a blue jelly bean given that a purple jelly bean was already chosen.

The probability of choosing a purple jelly bean is 8/20 = 2/5.

The probability of choosing a blue jelly bean given that a purple jelly bean was already chosen is 6/19. This is because there are only 6 blue jelly beans left after the purple jelly bean is eaten, and there are a total of 19 jelly beans left.

Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 2/5 * 6/19 = 12/95.

Another way to solve this problem is to use the following formula:

P(A and B) = P(A) * P(B | A)

Where:

P(A) is the probability of event A happening

P(B | A) is the probability of event B happening given that event A already happened

In this case, event A is choosing a purple jelly bean and event B is choosing a blue jelly bean.

Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is:

P(purple jelly bean) * P(blue jelly bean | purple jelly bean) = 2/5 * 6/19

= 12/95.

To learn more about probability here:

https://brainly.com/question/32117953

#SPJ12

Answer:

The height that cuts off the top 5% is 74.83 inches.

Step-by-step explanation:

We are given that in the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches.

Let X = heights of respondents

So, X ~ N([tex]\mu=69.9,\sigma^{2} =3^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean height = 69.9 inches

            [tex]\sigma[/tex] = standard deviation = 3.0 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we have to find the height that cuts off the top 5%, that means;

           P(X > [tex]x[/tex]) = 0.05   {where [tex]x[/tex] is the height that cuts off top 5%}

           P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

           P(Z > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

Now, in the z table the critical value of X that gives the area of top 5% is given as 1.6449.

So,         [tex]\frac{ x -69.9}{3} = 1.6449[/tex]

              [tex]x -69.9= 1.6449 \times 3[/tex]

                 [tex]x[/tex] = 69.9 + 4.9347 = 74.83

Hence, the height that cuts off the top 5% is 74.83 inches.

Answer:

[tex]a. \ H_o:p=0.45, \ \ \ \ H_a:p\neq 0.45\\\\b.\ \hat p=0.2209\\\\c. \ Yes\ (-4.2706<-1.96)[/tex]

Step-by-step explanation:

a. The professor's claim is that 45% first-timers fail his test. The null hypothesis is therefore stated as:

[tex]H_o:p=0.45[/tex]

-The alternative hypothesis is that more or less people fail the test as opposed to the professor's exact claim, hence:

[tex]H_a:p\neq 0.45[/tex]

b. To compute the P-value we use the z-value for a 95% confidence level:

[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]

#The proportion of failures in the sample of 86 is 19:

[tex]\hat p=\frac{19}{86}\\\\=0.2209[/tex]

The z-value is calculated as:

[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}[/tex]

[tex]=\frac{0.2209-0.45}{\sqrt{\frac{0.45(1-0.45)}{86}}}\\\\\\=-4.2706[/tex]

-4.2706 is less than the stated confidence level for the given 45% proportion and greatly differs from it.

- Reject the null hypothesis as there is enough evidence to reject the claim.

-Hence,Yes, Professor Brown can conclude that percentage  of failures differs from 45%.