Answer:
5.8 years
Step-by-step explanation:
The sampling distribution of the sample means has a mean that is equal to mean of the population from which the sample has been drawn.
study of elementary school students reports that the mean age at which children begin reading is 5.8 years with a standard deviation of 0.7 years.
This means the population mean is
[tex] \mu = 5.8 \: years[/tex]
and the population standard deviation is
[tex] \sigma = 0.7 \: years[/tex]
If a sampling distribution is created using samples of the ages at which 61 children begin reading, the mean of the sampling distribution of the sample mean will be
[tex]5.8 \: years[/tex]
The mean of the sampling distribution of sample means can be calculated by dividing the mean of the population by the square root of the sample size.
Explanation:To find the mean of the sampling distribution of sample means, we need to divide the mean of the population by the square root of the sample size. In this case, the mean of the population is 5.8 years and the sample size is 61 children. So, the mean of the sampling distribution of sample means can be calculated as:
Mean of sampling distribution of sample means = 5.8 years / sqrt(61) ≈ 0.745 years
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Analyze the diagram below and complete the instructions that follow.
and are similar. Find the value of x.
A.
5
B.
15
C.
60
D.
240
Please select the best answer from the choices provided
A
B
C
D
In how many ways can Susan arrange 7 books into 5 slots on her bookshelf?
Answer:
2520Step-by-step explanation:
This is permutation question
The formula for it:
N = b!/(b-s)!, where N- number of ways, b- number of books, s- number of slotsFinding the answer:
N = 7!/(7-5)! = 7!/2! = 7*6*5*4*3 = 2520Please help :(
There are 10^9 bytes in a gigabyte. There are 10^6 bytes in a megabyte. How manny times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?
answer choices above^^^
Answer:
In the screenshot you have the right answer, it is indeed 1000 times greater
Step-by-step explanation:
The mean crying time of infants during naptime at a local preschool is 12 mins. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8 ± 4.6 (M ± SD) minutes. Test whether this new naptime routine reduced crying time at a 0.05 level of significance.A) The new naptime routine significantly reduced crying time, t(24) = ?4.35, p <0.05.B) The new naptime routine did not reduce crying time, t(24) = ?4.35, p < 0.05.C) The new naptime routine did not reduce crying time, t(24) = 0.92, p > 0.05.D) The new naptime routine significantly reduce crying time, t(24) = 0.92, p < 0.05.
Answer:
Step-by-step explanatio n: ummmoirnd iehcn
A garden shop determines the demand function q = D(x) = 5x + 200 / 30x + 11 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.
(a) Find the elasticity.
(b) Find the elasticity when x = 2.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?
Answer: a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.
Step-by-step explanation:
Since we have given that
[tex]D(x)=\dfrac{5x+200}{30+11}[/tex]
So, derivative w.r.t x would be
[tex]D'(x)=\dfrac{5(30x+11)-30(5x+200)}{(30x+11)^2}\\\\D'(x)=\dfrac{150x+55-150x-6000}{(30x+11)^2}\\\\D'(x)=\dfrac{5945}{(30x+11)^2}[/tex]
As we know that
[tex]E(x)=\dfrac{-xD'(x)}{D(x)}\\\\\\E(x)=\dfrac{\dfrac{-(-)5945x}{(30x+11)^2}}{\dfrac{5x+200}{30x+11}}\\\\\\E(x)=\dfrac{5945x}{(30x+11)(5x+200)}[/tex]
(b) Find the elasticity when x = 2.
So, we put x = 2, we get that
[tex]E(2)=\dfrac{5945\times 2}{(30(2)+11)((5(2)+200))}\\\\E(2)=\dfrac{11890}{(60+11)(10+200)}\\\\E(2)=\dfrac{11890}{71\times 210}\\\\E(2)=\dfrac{11890}{14910}\\\\E(2)=0.7975[/tex]
Since, 0.7975 < 1, so the demand is inelastic.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?
The total revenue will also increase with increase in price.
As total revenue = [tex]price\times quantity[/tex]
Hence, a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.
This problem involves the calculation of the elasticity of a demand function using the derivative of the function. The elasticity is then used to analyze the effect on the total revenue when the price changes. The elasticity at a specific point is calculated and used for further analysis.
Explanation:For part (a), to find the elasticity of the demand function, we need to use the formula for the price elasticity of demand, which is E = (dQ/dX) * (X/Q). Here, dQ/dX is the derivative of the demand function concerning X. This needs to be calculated first. The value of E provides us with the measure of elasticity.
For part (b), when x = 2 we substitute this value into the formula for E to get the elasticity at x = 2.
For part (c), based on the concept of elasticity, if E > 1, the demand is said to be elastic and a price decrease will result in an increase in total revenue, and vice versa. If E < 1, the demand is said to be inelastic and a price decrease will result in a decrease in total revenue, and vice versa. So, after calculating E at x = 2, we can use it to determine the effect on total revenue.
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Megan finds a bag of 24 craft bows at the store. The bag indicates that 23 of the bows are striped. Megan wants to know the number of bows in the package that are striped. Select ALL the statements that are true. A Megan can divide the number 3 by 24 and then multiply the result by 2 to find the number of striped bows. B Megan can divide the number 24 by 3 and then multiply the result by 2 to find the number of striped bows. C Megan can multiply the number 24 by 2 and then divide the result by 3 to find the number of striped bows. D Megan can multiply the number 24 by 3 and then divide the result by 2 to find the number of striped bows. E The number of striped bows in the package is 36. F The number of striped bows in the package is 16.
Answer:
B
Step-by-step explanation:
In each part, find the area under the standard normal curve that lies between the specified z-score, sketch a standard normal curve, and shade the area of interest.
a. minus1 and 1
b. minus2 and 2
c. minus3 and 3
Answer:
a) [tex] P(-1<Z<1)= P(Z<1) -P(Z<-1)= 0.841-0.159= 0.682[/tex]
b) [tex] P(-2<Z<2)= P(Z<2) -P(Z<-2)= 0.977-0.0228= 0.954[/tex]
c) [tex] P(-3<Z<3)= P(Z<3) -P(Z<-3)= 0.999-0.0013= 0.998[/tex]
The results are on the fogure attached.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Part a
For this case we want to find this probability:
[tex] P(-1<Z<1)[/tex]
And we can find this probability with this difference:
[tex] P(-1<Z<1)= P(Z<1) -P(Z<-1)[/tex]
And if we find the probability using the normal standard distribution or excel we got:
[tex] P(-1<Z<1)= P(Z<1) -P(Z<-1)= 0.841-0.159= 0.682[/tex]
Part b
For this case we want to find this probability:
[tex] P(-2<Z<2)[/tex]
And we can find this probability with this difference:
[tex] P(-2<Z<2)= P(Z<2) -P(Z<-2)[/tex]
And if we find the probability using the normal standard distribution or excel we got:
[tex] P(-2<Z<2)= P(Z<2) -P(Z<-2)= 0.977-0.0228= 0.954[/tex]
Part c
For this case we want to find this probability:
[tex] P(-3<Z<3)[/tex]
And we can find this probability with this difference:
[tex] P(-3<Z<3)= P(Z<3) -P(Z<-3)[/tex]
And if we find the probability using the normal standard distribution or excel we got:
[tex] P(-3<Z<3)= P(Z<3) -P(Z<-3)= 0.999-0.0013= 0.998[/tex]
Final answer:
The question asks to find the area under the standard normal curve for specific z-score ranges. Using the empirical rule, we conclude that respective areas for those ranges are approximately 68%, 95%, and 99.7%. The exact areas can be found using a Z-table.
Explanation:
The question involves finding the area under the standard normal curve between specified z-scores. This is a fundamental concept in statistics, often used to find probabilities related to normally distributed data.
For a z-score between -1 and 1, approximately 68% of the area under the standard normal curve is contained since the empirical rule states that about 68 percent of values lie within one standard deviation of the mean in a normal distribution.For a z-score between -2 and 2, approximately 95% of the area under the curve is contained, as about 95% of the values lie within two standard deviations of the mean.For a z-score between -3 and 3, about 99.7% of the area is contained, reflecting the fact that about 99.7% of values in a normal distribution lie within three standard deviations of the mean.To find the exact areas based on the z-scores, we can refer to the Z-table of Standard Normal Distribution. This table lists the cumulative probabilities from the mean up to a certain z-score. By looking up the area to the left of each positive z-score and doubling it, we can get the approximate area between the negative and positive z-scores mentioned above.
A teacher used the change of base formula to determine whether the equation below is correct.
(log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3
Which statement explains whether the equation is correct?
Answer:
The equation is correct
Step-by-step explanation:
The equation, written as:
[log_2 (10)][log_4 (8)][log_10 (4)] = 3
Consider the change of base formula:
log_a (x) = [log_10 (x)]/ [log_10 (a)]
Applying the change of base formula to change the expressions in base 2 and base 4 to base 10.
(1)
log_2 (10) = [log_10 (10)]/[log_10 (2)]
= 1/[log_10 (2)]
(Because log_10 (10) = 1)
(2)
log_4 (8) = [log_10 (8)]/[log_10 (4)]
Now putting the values of these new logs in base 10 into the left-hand side of original equation to verify if we have 3, we have:
[log_10 (2)][log_8 (4)][log_10 (4)]
= [1/ log_10 (2)][log_10 (8) / log_10 (4)][log_10 (4)]
= [1/log_10 (2)] [log_10 (8)]
= [log_10 (8)]/[log_10 (2)]
= [log_10 (2³)]/[log_10 (2)]
Since log_b (a^x) = xlog_b (a)
= 3[log_10 (2)]/[log_10 (2)]
= 3 as required
Therefore, the left hand side of the equation is equal to the right hand side of the equation.
Answer:
B on E2020.
Step-by-step explanation:
A circle with radius four has a sector with a central angle of 8/5 pi radians. what is area of the sector
Answer:
area of sector = 40.192 unit²
Step-by-step explanation:
Area of a sector = ∅/360 × πr²
where
∅ = angle in degree
r = radius
Area of sector when ∅ = radian
area of a sector = 1/2r²∅
where
∅ = radian
r = radius
area of sector = 1/2 × 4² × 8/5 × π
area of sector = 1/2 × 16 × 8/5 × π
area of sector = 128/10 × π
area of sector = 12.8 × π
area of sector = 12.8 × 3.14
area of sector = 40.192 unit²
Check all that apply?
Answer:
–11 and 2
Step-by-step explanation:
observe
x² + 9x – 22 = 0
(x + 11)(x – 2) = 0
x = –11 or x = 2
What is the selling price if the original cost is $145 and the markup is 150%? PLEASE HELP!! :(
Answer:
$362.50
Profit: $217.50
Step-by-step explanation:
The measurement of a side of a square is found to be 10 centimeters, with a possible error of 0.07 centimeter. (a) Approximate the percent error in computing the area of the square. % (b) Estimate the maximum allowable percent error in measuring the side if the error in computing the area cannot exceed 2.7%. %
Answer:
a) [tex]\delta = 1.4\,\%[/tex], b) [tex]\delta_{max} = 1.35\,\%[/tex]
Step-by-step explanation:
a) The area formula for a square is:
[tex]A =l^{2}[/tex]
The total differential for the area is:
[tex]\Delta A = \frac{\partial A}{\partial l}\cdot \Delta l[/tex]
[tex]\Delta A = 2\cdot l \cdot \Delta l[/tex]
The absolute error for the area of the square is:
[tex]\Delta A = 2\cdot (10\,cm)\cdot (0.07\,cm)[/tex]
[tex]\Delta A = 1.4\,cm^{2}[/tex]
Thus, the relative error is:
[tex]\delta = \frac{\Delta A}{A}\times 100\,\%[/tex]
[tex]\delta = \frac{1.4\,cm^{2}}{100\,cm^{2}} \times 100\,\%[/tex]
[tex]\delta = 1.4\,\%[/tex]
b) The maximum allowable absolute error for the area of the square is:
[tex]\Delta A_{max} = \left(\frac{\delta}{100} \right)\cdot A[/tex]
[tex]\Delta A_{max} = \left(\frac{2.7}{100} \right)\cdot (100\,cm^{2})[/tex]
[tex]\Delta A_{max} = 2.7\,cm^{2}[/tex]
The maximum allowable absolute error for the length of a side of the square is:
[tex]\Delta l_{max}= \frac{\Delta A_{max}}{2\cdot l}[/tex]
[tex]\Delta l_{max} = \frac{2.7\,cm^{2}}{2\cdot (10\,cm)}[/tex]
[tex]\Delta l_{max} = 0.135\,cm[/tex]
Lastly, the maximum allowable relative error is:
[tex]\delta_{max} = \frac{\Delta l_{max}}{l}\times 100\,\%[/tex]
[tex]\delta_{max} = \frac{0.135\,cm}{10\,cm} \times 100\,\%[/tex]
[tex]\delta_{max} = 1.35\,\%[/tex]
100 POINTS HELP ME PLEASE!!!!!! DONT HAVE ALOT OF TIME HURRY PLEASE!!!!!!!!!!!!!
100 POINTS!!!!!
Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below.
A figure can be broken into a triangle and rectangle. The rectangle has a base of 200 millimeters and height of 50 millimeters. The triangle has a base of 50 millimeters and height of 100 millimeters.
What will be the area of the front face of his model?
2,500 square millimeters
10,000 square millimeters
12,500 square millimeters
15,000 square millimeters
Answer:
12,500 square millimeters
Step-by-step explanation:
Answer:
c(12,500)
Step-by-step explanation:
In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?
Quadratic formula: x =
x = 5
x = 5
x = 5
x = 5
Answer:
Step-by-step explanation:
quadratic equation: ax² + bx + c =0
x' = [-b+√(b²-4ac)]/2a and x" = [-b-√(b²-4ac)]/2a
6 = x² – 10x ; x² - 10x -6 =0
(a=1, b= - 10 and c = - 6
x' = [10+√(10²+4(1)(-6)]/2(1) and x" = [10-√(10²+4(1)(-6)]/2(1)
x' =5+√31 and x' = 5-√31
The locations, given in polar coordinates, for two ships are (8 mi, 639) and (8 mi, 1239). Find the distance between the two
ships,
a. 64 8 mi
C. 11.31 mi
b. 3600.00 mi
d. 4.14 mi
Please select the best answer
Answer:
A. [tex]\sqrt{64}=8[/tex] miles
Step-by-step explanation:
Given two Cartesian coordinates [tex](x_1,y_1)\&(x_2,y_2)[/tex], the distance between the points is given as:
[tex]d = \sqrt{((x_1-x_2)^2+(y_1-y_2)^2)}[/tex]
Converting to polar coordinates
[tex](x_1,y_1) = (r_1 cos \theta_1, r_1 sin \theta_1)\\(x_2,y_2) = (r_2 cos \theta_2, r_2 sin \theta_2)[/tex]
Substitution into the distance formula gives:
[tex]\sqrt{((r_1 cos\theta_1-r_2 cos \theta_2)^2+(r_1 sin \theta_1-r_2 sin \theta_2)^2}\\=\sqrt{(r_1^2+r_2^2-2r_1r_2(cos \theta_1 cos \theta_2+sin\theta_1 sin \theta_2) }\\= \sqrt{r_1^2+r_2^2-2r_1r_2cos (\theta_1 -\theta_2)}[/tex]
In the given problem,
[tex](r_1,\theta_1)=(8 mi, 63^0) \:and\: (r_2,\theta_2)=(8 mi, 123^0 ).[/tex]
[tex]Distance=\sqrt{8^2+8^2-2(8)(8)cos (63 -123)}\\=\sqrt{128-128cos (-60)}\\=\sqrt{64}=8 mile[/tex]
The closest option is A. [tex]\sqrt{64}=8[/tex] miles
-1.9+4+(-1.6) simplify the expression
Answer:
.5
Step-by-step explanation:
-1.9+4=2.1
2.1+(-1.6)=.5
WILL GIVE BRAINLIEST
A new car can go 490 miles on 10 gallons of gas. How many miles can it go on 55 gallons of gas?
Answer:
2695 miles
Step-by-step explanation:
The car can travel 2,695 miles on 55 gallons of gas.
To determine how many miles a car can go on 55 gallons of gas if it can go 490 miles on 10 gallons, we need to find the car's miles per gallon (mpg) and then use that to calculate the distance for 55 gallons.
First, calculate the miles per gallon (mpg):
mpg = 490 miles / 10 gallons = 49 miles per gallon
Now, use the mpg to find the distance the car can travel on 55 gallons:
Distance = 49 miles per gallon * 55 gallons = 2,695 miles
Therefore, the car can go 2,695 miles on 55 gallons of gas.
HELLPP
A cardboard box has the shape of a rectangular prism. Its height is 10
inches. Its length is three times its width. The volume is 540 cubic inches.
Find the width of the box. *
Answer
Step-by-step explanation:
H*W*L
280=7*W*(6+W)
280=42W+7W^2
40=6w+w^2
W^2+6W-40=0
(W-4)(W+10)=0
W=4
We can only use positive results
L=6+W
L=4+6=10
Given that, the height of the cardboard box=10 inches and volume = 540 cubic inches.
Let the width of the cardboard box be x, then the length will be 3x.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is Volume=Length×Width×Height.
Now, 540=10×x×3x
⇒x²=18
⇒x=3√2 inches.
Therefore, the width of a cardboard box is 3√2 inches.
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What is the area of the following circle
Answer:
16*pi=50.24
Step-by-step explanation:
Answer:
16* pi = 50.24
Step-by-step explanation:
The divisor of 0.004 is almost zero. What does this tell you about the quotient?
Answer:
Its magnitude will be larger than 0.004.
Step-by-step explanation:
When a divisor is less than 1, the quotient will be greater than the dividend.
When the divisor is "almost zero", the quotient will be much greater than the dividend. Here, the dividend may be considered to be "almost zero", so we cannot say anything about the actual quotient except to say its magnitude will be greater than the dividend.
_____
The dividend is positive, so the quotient will have the same sign as the divisor. (Negative divisors can be "almost zero," too.)
Now focus on the boundary of D, and solve for y2. Restricting f(x,y) to this boundary, we can express f(x,y) as a function of a single variable x. What is this function and its closed interval domain?
Answer:
At critical point in D
a
[tex](x,y) = (0,0)[/tex]
b
[tex]f(x,y) = f(x) =11 -x^2[/tex]
where [tex]-1 \le x \le 1[/tex]
c
maximum value 11
minimum value 10
Step-by-step explanation:
Given [tex]f(x,y) =10x^2 + 11x^2[/tex]
At critical point
[tex]f'(x,y) = 0[/tex]
=> [tex][f'(x,y)]_x = 20x =0[/tex]
=> [tex]x =0[/tex]
Also
[tex][f'(x,y)]_y = 22y =0[/tex]
=> [tex]y =0[/tex]
Now considering along the boundary
[tex]D = 1[/tex]
=> [tex]x^2 +y^2 = 1[/tex]
=> [tex]y =\pm \sqrt{1- x^2}[/tex]
Restricting [tex]f(x,y)[/tex] to this boundary
[tex]f(x,y) = f(x) = 10x^2 +11(1-x^2)^{\frac{2}{1} *\frac{1}{2} }[/tex]
[tex]= 11-x^2[/tex]
At boundary point D = 1
Which implies that [tex]x \le 1[/tex] or [tex]x \ge -1[/tex]
So the range of x is
[tex]-1 \le x \le 1[/tex]
Now along this this boundary the critical point is at
[tex]f'(x) = 0[/tex]
=> [tex]f'(x) = -2x =0[/tex]
=> [tex]x=0[/tex]
Now at maximum point [tex](i.e \ x =0)[/tex]
[tex]f(0) =11 -(0)[/tex]
[tex]= 11[/tex]
For the minimum point x = -1 or x =1
[tex]f(1) = 11 - 1^2[/tex]
[tex]=10[/tex]
[tex]f(-1) = 11 -(-1)^2[/tex]
[tex]=10[/tex]
Which is a correct first step for solving this equation?
2 + 7 = 2x + 5 – 4x
Step-by-step explanation:
Bringing like terms on one side
2 + 7 - 5 = 2x - 4x
9 - 5 = - 2x
4 = - 2x
4/ - 2 = x
- 2 = x
The fictional rocket ship Adventure is measured to be 65 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c. As rocket ship Adventure passes by the space dock, the ship's captain flashes a flashlight at 2.00-s intervals as measured by space-dock personnel. Part A How often does the flashlight flash relative to the captain
Answer:
a) t₀ = 1.73205 s
b) 1.0 C
Step-by-step explanation:
(A)
The time dilation (t) observed by an observer at rest relative to the time (t₀) measured by observer in motion is;
[tex]t = \frac{t_0}{\sqrt{1 - \frac{V^2}{C^2}}}[/tex]
[tex]t_0 = t \sqrt{1 - \frac{V^2}{C^2}}[/tex] time measured by captain
⇒ [tex]t_0 = 2.0 \sqrt{1 - \frac{0.5^2C^2}{C^2}}[/tex] V = 0.5 c
⇒ t₀ = 1.73205 s
(B)
Speed of the light never exceeds by its real value. The speed of the light in any frame of reference is constant.
∵ It will be "1.0C" or just "C"
Does anyone know this?
Answer:
A. 5 * 1/7
Step-by-step explanation:
When solving division, you can also multiply by the reciprocal of the second number to get the same answer.
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. If students have only 90 minutes to complete the exam, what percentage of the class will not finish the exam in time?
Answer:
Hence total of 10 students are not able to complete the exam.
Step-by-step explanation:
Given:
Mean for completing exam =80 min
standard deviation =10 min.
To find:
how much student will not complete the exam?
Solution:
using the Z-table score we can calculate the required probability.
Z=(Required time -mean)/standard deviation.
A standard on an avg class contains:
60 students.
consider for 70 mins and then 90 mins (generally calculate ± standard deviation of mean)(80-10 and 80+10).
1)70 min
Z=(70-80)/10
Z=-1
Now corresponding p will be
P(z=-1)
=0.1587
therefore
Now for required 90 min will be
Z=(90-80)/10
=10/10
z=1
So corresponding value of p is
P(z<1)=0.8413
this means 0.8413 of 60 students are able to complete the exam.
0.8413*60
=50.47
which approximate 50 students,
total number =60
and total number student will able to complete =50
Total number of student will not complete =60-50
=10.
About 15.87% of college students are expected not to finish the final examination within the 90-minute time limit, based on the properties of the normal distribution with a mean of 80 minutes and a standard deviation of 10 minutes.
Explanation:The student's question involves using the properties of the normal distribution to determine the percentage of students who will not finish a final examination in the given time frame.
To compute this, we need to calculate the z-score that corresponds to the 90-minute time limit. The z-score formula is:
Z = (X - μ) / σ
where X is the value of interest, μ (mu) is the mean, and σ (sigma) is the standard deviation. Plugging in the numbers:
Z = (90 - 80) / 10 = 1
A z-score of 1 corresponds to a percentile of approximately 84.13%, meaning about 84.13% of students will finish within 90 minutes. To find the percentage that will not finish in time, we subtract this from 100%:
100% - 84.13% = 15.87%
Therefore, approximately 15.87% of the class will not finish the exam in time.
is 119x10-3 to the power a scientific notation? yes or no? explain
Answer:
Yes, if I'm assuming that it was written as [tex]119*10^-3[/tex], then this is a basis for a scientific notation.
Half of the sum of 32 and 2
Answer:
17
Step-by-step explanation:
32+2=34
34/2= 17
Half of the sum of 32 and twice a number 'x' expressed as '2ans' would be calculated by adding 32 and 2x and then dividing by 2, resulting in the expression 16 + x.
The question asks to find half of the sum of 32 and an unspecified number (mentioned as '2ans'). Assuming '2ans' means twice the number 'ans', which can be represented as 2x, where 'x' is the particular value of 'ans'. First, calculate the sum of 32 and 2x, and then divide that sum by two to find half of it.
The steps to solve this are:
Calculate the sum: 32 + 2x.
To find half of the sum, divide by 2: (32 + 2x) / 2.
Simplify the expression: 16 + x.
Therefore, half of the sum of 32 and twice a number 'x' (2x) is 16 + x.
Kelsey’s bank changed her $17.50
a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15. a sample of 36 students was selected. what is the probability that the average time spent studying for the sample was between 29.0 and 30 hours studying?
Answer:
Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.
Step-by-step explanation:
We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.
A sample of 36 students was selected.
Let [tex]\bar X[/tex] = sample average time spent studying
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean hours spent studying = 25 hours
[tex]\sigma[/tex] = standard deviation = 15 hours
n = sample of students = 36
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, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < [tex]\bar X[/tex] < 30 hours)
P(29 hours < [tex]\bar X[/tex] < 30 hours) = P([tex]\bar X[/tex] < 30 hours) - P([tex]\bar X[/tex] [tex]\leq[/tex] 29 hours)
P([tex]\bar X[/tex] < 30 hours) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] < [tex]\frac{ 30-25}{\frac{15}{\sqrt{36} } }} }[/tex] ) = P(Z < 2) = 0.97725
P([tex]\bar X[/tex] [tex]\leq[/tex] 29 hours) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{ 29-25}{\frac{15}{\sqrt{36} } }} }[/tex] ) = P(Z [tex]\leq[/tex] 1.60) = 0.94520
So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.
Therefore, P(29 hours < [tex]\bar X[/tex] < 30 hours) = 0.97725 - 0.94520 = 0.0321
Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.