An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with μ = 0.50 and σ = 0.08. (Round your answers to four decimal places.) (a) What is the probability that the concentration exceeds 0.60?

Answer:

the answer is 44

you don't have the answer choice

The probability that the first digit of a three-digit locker combination is less than 3 is 2/9, because there are 2 favorable digits (1 and 2) out of 9 possible non-zero digits, option C.

The question is asking about the probability that the first digit of a three-digit locker combination is less than 3, given that none of the digits can be 0. Since the digits can range from 1 to 9 (inclusive), there are a total of 9 possible digits for the first position. We are interested in the digits 1 and 2, which are the only digits less than 3. Therefore, there are 2 favorable outcomes.

To calculate the probability, we use the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is 2 (favorable outcomes) divided by 9 (possible outcomes), which simplifies to:

Probability = 2/9, option C.

Answer:

False

Step-by-step explanation:

Because with the lines on the outside automatically changes the number to a positive number so, therefor the numbers are equal hope this help.

Rate brainlest plz

Michaela's statement that |3| is bigger than |-3| is true.

Michaela's assertion that |3| is greater than |-3| is accurate. The absolute value of a number represents its distance from zero on the number line. In this case, |3| signifies a 3-unit distance from zero, and |-3| also corresponds to a 3-unit distance from zero. Since both values are equidistant from zero, their magnitudes are equal. Consequently, |3| and |-3| both have a value of 3, emphasizing that the absolute value of a number signifies its distance from zero, regardless of its sign, and in this case, both distances are identical at 3 units.

https://brainly.com/question/18731489

#SPJ11

Answer:

C. 31

Step-by-step explanation:

(570.7 - n) ÷ 16

(570.7 - 74.7) ÷ 16

496 ÷ 16

31

Answer:

$220?

Step-by-step explanation:

Answer$220

Step-by-step explanation:

77/7=$11 so $11x20=220

Answer:

2.9106

Step-by-step explanation:

According to the information of the problem

Year 75   76   77   78    79    80    81      82 83 84 85 86 87

Lean 642 644 656  667   673  688 696  698 713 717 725 742 757

If you use a linear regressor calculator you find that approximately

[tex]y = 9.318 x - 61.123[/tex]

so you just find [tex]x = 18[/tex]  and then the predicted value would be 106mm

therefore the predicted value for the lean in 1918 was 2.9106

Answer:

168

Step-by-step explanation:

GIVEN: Nadia is making a rectangular moisac out of [tex]\frac{1}{2}[/tex] inch by [tex]\frac{1}{2}[/tex] inch tiles. The rectangle is [tex]12[/tex] inches long and [tex]3\frac{1}{2}[/tex] inches wide.

TO FIND: How many tiles will Nadia use to cover the rectangle completely.

SOLUTION:

Area of rectangular moisac[tex]=\text{length}\times\text{width}[/tex]

                                            [tex]=12\times3\frac{1}{2}=\frac{12\times7}{2}[/tex]

                                            [tex]=42 \text{ inch}^2[/tex]

Area of one   tile [tex]=\text{side}^2[/tex]

                           [tex]=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\text{ inch}^2[/tex]

According to question

Total tiles required [tex]=\frac{\text{Area of rectangular moisac}}{\text{Area of one tile}}[/tex]

                                [tex]=\frac{42}{\frac{1}{4}}=42\times4[/tex]

                                [tex]=168[/tex] tiles

Hence, 168 tiles are required to completely cover the rectangular moisac.

Answer:

95% confidence interval for the difference in the proportion is [-0.017 , 0.697].

Step-by-step explanation:

We are given that a simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were "totaled," meaning that the cost of repairs is greater than the value of the car.

Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled.

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;

                             P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of small cars that were totaled = [tex]\frac{8}{12}[/tex] = 0.67

[tex]\hat p_2[/tex] = sample proportion of large cars that were totaled = [tex]\frac{5}{15}[/tex] = 0.33

[tex]n_1[/tex] = sample of small cars = 12

[tex]n_2[/tex] = sample of large cars = 15

[tex]p_1[/tex] = population proportion of small cars that are totaled

[tex]p_2[/tex] = population proportion of large cars that were totaled

Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.

So, 95% confidence interval for the difference between population population, ([tex]p_1-p_2[/tex]) is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                    of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95

P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]p_1-p_2[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95

95% confidence interval for [tex]p_1-p_2[/tex] = [[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] , [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]]

= [[tex](0.67-0.33)-1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex] , [tex](0.67-0.33)+1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex]]

= [-0.017 , 0.697]

Therefore, 95% confidence interval for the difference between proportions l and 2 is [-0.017 , 0.697].

Answer:

Step-by-step explanation:

Given that,

A regular heptagon, a heptagon has 7 sides and since it is a regular heptagon, then, it has equal sides

n = 7, number of sides

Each sides of the heptagon has a length of 13.9

s= 13.9

The apothem is 14.4

Apothem is a line from the centre of a regular polygon at right angles to any of its sides.

r = 14.4

The area of a regular heptagon can be calculated using

Area = ½ n•s•r

Where n is the number of sides

s- is the length of the sides

r Is the apothem

Then,

A = ½ × 7 × 13.9 × 14.4

A = 700.56 square units

To the nearest whole number, I.e no decimal points

A = 701 Square units

X > 0

sdjkfgsdjfjkdfnejnwsfjdnsk it made me write more

Since the blue line points to numbers more positive then 0, it would be a greater then. Since the dot is open it would be greater then and not equal to.

Therefore the answer is B, x > 0

In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are [tex]\binom44\binom{48}1=48[/tex] possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by [tex]\binom{13}1=13[/tex]. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability

[tex]\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024[/tex]

There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing [tex]\binom41\binom{48}4=778,320[/tex] possible hands. Exactly 2 aces are drawn in [tex]\binom42\binom{48}3=103,776[/tex] hands. And so on. This gives a total of

[tex]\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656[/tex]

possible hands containing at least 1 ace, and hence B occurs with probability

[tex]\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412[/tex]

The product of these probability is approximately 0.000082.

A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. [tex]P(A\cap B)=P(A)P(B)[/tex]. This happens if

The above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So [tex]A\cap B[/tex] consists of 96 possible hands, which occurs with probability

[tex]\dfrac{96}{\binom{52}5}\approx0.0000369[/tex]

and so the events A and B are NOT independent.

The events A and B in the given scenario are not independent. This determination is based on the principle of sampling without replacement, where drawing a four of a kind is likely to influence the probability of drawing an ace.

Two events A: the hand is a four of a kind, and B: at least one of the cards in the hand is an ace, are defined in a situation where a 5-card hand is dealt from a perfectly shuffled 52-card deck. To determine if these events are independent, we need to check if the occurrence of event A affects the occurrence of event B.

In sampling with replacement, each member of a population is replaced after it is picked. However, dealing a 5-card hand from a deck of cards is an example of sampling without replacement, meaning that each card may only be chosen once, causing the events to be considered as not independent.

It is highly probable that drawing a four of a kind will influence the likelihood of drawing an ace. Hence, the events A and B are not independent.

https://brainly.com/question/30905572

#SPJ3

Answer:

[tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = \frac{5}{4}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \frac{10}{x^2} \\\left[ 4 ,\ 8 \right][/tex]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

p(x) = x^4  - x^3  - 9x^2  - 11x  - 4

Step-by-step explanation:

You are saying there are  3 roots of  x = -1   and one  x = 4 root

so...

p(x)  =  [(x + 1)^3 ] * (x - 4)

p(x) =  (xxx  + 3xx  + 3x + 1 )*(x- 4)

p(x) = x^4  + 3 x^3  + 3x^2  + x  -  4x^3 - 12xx  - 12x  - 4

p(x) = x^4  - x^3  - 9x^2  - 11x  - 4

Answer: yes

Step-by-step explanation:

do u by chance still have access to those units on odyssey would love to get the answers lol.

Answer:

$332.82

Step-by-step explanation:

We will use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, we change 3.4% into a decimal:

3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

[tex]A=200(1+\frac{0.034}{12})^{12(15)}[/tex]

[tex]A=332.82[/tex]

Your balance after 15 years will be $332.82

Answer:

The answer is there is a difference in the mean production rate by shift

Step-by-step explanation:

The level of significance is actually very low since the same production level is maintained for each of the 5 workers at the same time in the afternoon.

As for the other shifts, that is, the day shift and the night shift, the level of significance varies according to the production established by each worker.h

Answer:

The zeros for this function are x = -1 and x = 1.67

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = 3x^{2} - 2x - 5[/tex]

The zeros of the function are the values of x for which

[tex]f(x) = 0[/tex]

Then

[tex]3x^{2} - 2x - 5 = 0[/tex]

This means that [tex]a = 3, b = -2, c = -5[/tex]

Then

[tex]\bigtriangleup = (-2)^{2} - 4*3*(-5) = 64[/tex]

[tex]x_{1} = \frac{-(-2) + \sqrt{64}}{2*3} = 1.67[/tex]

[tex]x_{2} = \frac{-(-2) - \sqrt{64}}{2*3} = -1[/tex]

The zeros for this function are x = -1 and x = 1.67

Bruh. More information is needed to answer that question. We need to know the rate of change.

Answer:

[tex](D)E[ X ] =np.[/tex]

Step-by-step explanation:

Given a binomial experiment with n trials and probability of success​ p,

[tex]f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n[/tex]

[tex]E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}[/tex]

Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:

[tex]E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}[/tex]

Now,

[tex]x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)[/tex]

Substituting,

[tex]E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}[/tex]

Factoring out the n and one p from the above expression:

[tex]E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}[/tex]

Representing k=x-1 in the above gives us:

[tex]E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}[/tex]

This can then be written by the Binomial Formula as:

[tex]E[ X ] = (np) (p +(1 - p))^{n -1 }= np.[/tex]

The correct formula for the expected number of successes in a binomial experiment with n trials and probability of success p is μ = np (Option D), which means that the expected number of successes is calculated by multiplying the total number of trials by the probability of success.

The formula for the expected number of successes in a binomial experiment with n trials and probability of success p is given by μ = np. In this formula, 'n' represents the number of trials, and 'p' is the probability of success on each trial. Therefore, the correct option, in this case, is D. Upper E (Upper X ) equals np.

This essentially means that the expected number of successes is obtained by multiplying the total number of trials by the probability of success. For instance, if you were to flip a coin (where the probability of getting heads is 0.5) 10 times, the expected number of times you'd get heads would be 0.5 * 10 = 5.

https://brainly.com/question/35646493

#SPJ3

Final answer:

Upon calculating the mean, range, mode, and median for both groups of house cats, we found that none of the statistics have greater values for Group 1 than for Group 2.

Explanation:

To determine which statistic has a greater value for Group 1 than Group 2 in a dataset containing the weights of house cats, we first need to calculate the mean, range, mode, and median for both groups.

Calculations for Group 1:

Calculations for Group 2:

When comparing the statistics, we can see that the range of Group 1 is smaller than that of Group 2, and the mean and median for Group 1 are also smaller than those for Group 2. The mode for both groups is the same with two values that repeat the most. Therefore, none of the statistics have greater values for Group 1 than for Group 2.

Answer:

4/5

Step-by-step explanation:

We can find the slope when given two points by using

m= (y2-y1)/(x2-x1)

  = (8-0)/(10-0)

  =8/10

  = 4/5

Answer:

4/5

Step-by-step explanation:

Answer:

Slope (m)= -12.5/5= -2.5

-12.5/5 in fraction form

or

-2.5 in decimal form

Step-by-step explanation:

slope (m)= -12.5/5= -2.5

the points belong as a decreasing linear function

equation: y= -2.5x-5

Answer:

$72

Step-by-step explanation:

Answer:

72.9  (mark me brainleist pls )

Step-by-step explanation:

81 x 0.10 = 8.1

81 - 8.1 = 72.9

Answer:

[tex] Test score_i= 557.8 +36.42 Income[/tex]

If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:

[tex] Test score_f = 557.8  + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]

And the net increase can be founded like this:

[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]

So then the net increase would be:

C. 0.36 points

Step-by-step explanation:

For this case we have the following linear relationship obtained from least squares between test scores and the student-teacher ratio:

[tex] Test score_i= 557.8 +36.42 Income[/tex]

If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:

[tex] Test score_f = 557.8  + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]

And the net increase can be founded like this:

[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]

So then the net increase would be:

C. 0.36 points

For a 1% increase in income, the test scores would increase by approximately 0.36 points based on the given regression equation. This is calculated by multiplying the coefficient of the natural logarithm of income, 36.42, with the decimal value of the percent change in income, which is 0.01.

The equation provided is a linear regression equation where the dependent variable, TestScore, is predicted based on the natural logarithm of the independent variable, Income. The coefficient of 36.42 in front of the natural logarithm indicates how much the dependent variable changes for a 1% change in the independent variable. To find the contribution to the test scores for a 1% increase in income, we need to use the fact that the derivative of the natural logarithm, Ln(x), with respect to x is 1/x, which means a change in income translates directly to the change in test score when multiplied by the coefficient.

So, for a small percentage change in income, approximately 1%, the corresponding change in TestScore is 36.42 multiplied by the percentage change in decimal form. Specifically, 0.01 × 36.42 = 0.3642 or approximately 0.36 points.

Answer:

.55M + 75 = the total cost

.55(300) + 75 = $240

Step-by-step explanation:

Answer:

the 90% of confidence intervals for the average salary of a CFA charter holder

 (1,63,775 , 1,80,000)

Step-by-step explanation:

Explanation:-

random sample of n = 49 recent charter holders

mean of sample (x⁻) =  $172,000

standard deviation of sample( S) = $35,000

Level of significance α= 1.645

90% confidence interval

[tex](x^{-} - Z_{\alpha } \frac{s}{\sqrt{n} } , x^{-} + Z_{\alpha } \frac{s}{\sqrt{n} })[/tex]

[tex](172000 - 1.645 \frac{35000}{\sqrt{49} } , 172000 +1.645 \frac{35000}{\sqrt{49} })[/tex]

on calculation , we get

(1,63,775 , 1,80,000)

The mean value lies between the 90% of confidence intervals

(1,63,775 , 1,80,000)

Answer:

6(1-r)

Step-by-step explanation:

8-6r+2

=6-6r

=6(1-r)

Answer:

The confidence level for this interval is 99%.

Step-by-step explanation:

The margin of error M has the following equation.

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level.

In this problem:

[tex]M = 25.76, \sigma = 100, n = 100[/tex]

So

[tex]25.76 = z*\frac{100}{\sqrt{100}}[/tex]

[tex]10z = 25.76[/tex]

[tex]z = 2.576[/tex]

Looking at the z table, [tex]z = 2.576[/tex] has a pvalue of 0.995.

So the confidence level is:

[tex]1 - 2(1 - 0.995) = 1 - 0.01 = 0.99[/tex]

The confidence level for this interval is 99%.

Answer:

5 ( 2 + 3x )

Step-by-step explanation:

1st step: Take the GCF of the equation 10+15x

2nd step: GCF means, taking the Greatest Common Factor out of BOTH the numbers in an equation. (GCF is 5 in this case.)

3rd step: Divide by the GCF that you got. (In this case, you have 10 +15x. You need to do 10/5, and 15x /5. (Note that ANYTHING multiplied by "x" can also be divided just like a regular number.)

4th step: Put the the number that you divided with for both numbers OUTSIDE parentheses. (Note in this case it is common.)

5th step: Check your work. PLEASE DO THIS STEP.

Check: 5( 2 + 3x )

5 x 2 = 10

5 x '3x' = 15x

So, the answer for this problem is: 5 ( 2 +3x )

Answer: 5( 2 + 3x)

Hope this helped you understand the basics of disributive property. And if you have another problem just like this, you can use the same rule as shown above. :)

Final answer:

Use the distributive property to factor out a common factor in 10 + 15x to get an equivalent expression.

Explanation:

To write an expression equivalent to 10 + 15x using the distributive property, you can factor out a common factor. Here’s how:

Factor out 5 from 10 and 15x: 10 + 15x = 5(2 + 3x)

Apply the distributive property to get the equivalent expression: 5(2 + 3x) = 5*2 + 5*3x = 10 + 15x

Answer:

The answer is option A.

Step-by-step explanation:

Subjective probability is defined as a probability which is derived from a person's own experience or belief without relying on any data or scientific calculation.

In the question, the situation given in option A is an example of subjective probability because the analyst is giving a probability based on his or her own belief without using any data at all.

The other options clearly state the probability is being calculated by relying on observations and data.

I hope this answer helps.

A subjective probability example is the belief of a sports analyst in the probability of one college team beating another, without prior data. This contrasts with objective probabilities based on statistical analysis or historical evidence.

The example of a subjective probability among the options given is when a sports analyst believes there is a 0.8 probability that College A will beat College B in their upcoming basketball game, despite there being no previous encounters between the two teams to base this on. This type of probability, which includes personal belief or judgment rather than empirical evidence and statistical analysis, contrasts with objective probabilities that rely on historical data, such as the probability of a 20-year old driver having an accident or the probability of drawing a specific card from a standard deck.

Subjective probability is used in situations where there is a lack of historical data or when assessing future events, making it a personal estimation. This approach is different from calculating probabilities based on observed outcomes and statistical independence, where the probability of events is determined through analysis and empirical evidence.

Final answer:

To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, use the Central Limit Theorem to approximate the distribution of sample means. Calculate the standard error using the formula: standard error = population standard deviation / sqrt(sample size). Then, standardize the sample mean using the z-score formula. Finally, find the probability using a standard normal distribution table or a calculator.Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.

Explanation:

To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).

First, we need to calculate the standard error, which is the standard deviation of the sampling distribution of the sample mean. The standard error is given by the formula: standard error = population standard deviation / sqrt(sample size). In this case, the population standard deviation is 368 miles, and the sample size is 44. Therefore, the standard error = 368 / sqrt(44) = 55.354 miles.

Next, we use the z-score formula to standardize the sample mean. The z-score = (sample mean - population mean) / standard error. Plugging in the given values, we get: z-score = (51 - 2643) / 55.354 = -0.3668.

Finally, we need to find the probability that the standardized sample mean (z-score) is less than -0.3668. We can use a standard normal distribution table or a calculator to find the corresponding probability. From the standard normal distribution table, we find that the probability corresponding to a z-score of -0.3668 is approximately 0.3595. Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.