The number of boots that 12 students had in their homes in Florida were recorded below:

A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing sam

professor190 [17]

Answer:

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A distribution of values is normal with a mean of 60 and a standard deviation of 16.

This means that $\mu = 60, \sigma = 16$

Samples of size 25:

This means that $n = 25, s = \frac{16}{\sqrt{25}} = 3.2$

Find the interval containing the middle-most 76% of sample means.

Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.

12th percentile:

X when Z has a p-value of 0.12, so X when Z = -1.175.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$-1.175 = \frac{X - 60}{3.2}$

$X - 60 = -1.175*3.2$

$X = 56.24$

88th percentile:

$Z = \frac{X - \mu}{s}$

$1.175 = \frac{X - 60}{3.2}$

$X - 60 = 1.175*3.2$

$X = 63.76$

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

3 0

3 years ago

9x-7i>3(3x-7u) Solve for I

kozerog [31]

Answer:

i < 3u

Step-by-step explanation:

3 0

2 years ago

QUESTION 2 Brewsky's is a chain of micro-breweries. Managers are interested in the costs of the stores and believe that the cost

Sever21 [200]

Answer:

b is the amount by which the costs of the stores (i.e. y) will increase whenever the number of customers patronizing the stores (i.e. x) increases by one.

Step-by-step explanation:

How is the letter b best described?

b is the amount by which the costs of the stores (i.e. y) will increase whenever the number of customers patronizing the stores (i.e. x) increases by one.

That is, b is the coefficient of letter x and it indicates that whenever there is a one unit increase in the number of customers patronizing the stores (i.e. x), the costs of the stores (i.e. y) will increase by $2.08.

To give an example, the regression equation in the question is expressed as:

y = a + bx ............................ (1)

Where;

y = the costs of the stores = ?

a = Intercept = $1,496

b = coefficient = $2.08

x = the number of customers patronizing the stores = ?

Assume x = 1, we can predict y by substituting the values to obtain y1 as follows:

y1 = $1,496 + ($2.08 * 1) = $1,496 + $2.08 = $1,498.08

Now, assume x increases by 1 to 2 i.e. x = 2, we can predict y by substituting the values to obtain y2 as follows:

y2 = $1,496 + ($2.08 * 2) = $1,496 + $4.16 = $1,500.16

The the change is y as a result of one unit increase in x from 1 to 2 can then be obtained as follow:

Change in y = y2 - y1 = $1,500.16 - $1,498.08 = $2.08.

This therefore cofirms that b indicates that whenever there is a one unit increase in the number of customers patronizing the stores (i.e. x), the costs of the stores (i.e. y) will increase by $2.08.

7 0

3 years ago

6th grade math! Helpppp

ruslelena [56]

Answer:

24 points per game

Step-by-step explanation:

you divide 96/4

3 0

3 years ago

Read 2 more answers

1. Simplify this expression: 13+ (-12) - (-5) = ? O A.-30 O B.6 O C.30 OD. -6

Virty [35]

Answer:

B.6

Step-by-step explanation:

When we add and subtract, we do it from left to right

13+ (-12) - (-5)

13+-12

13-12 = 1

1 - -5

A negative negative is a positive

1 +5

6

8 0

3 years ago

Read 2 more answers