Mathematics, 25.02.2020 23:32 johnsonkia873

The number of times that students go to the movies per year has mean is a normal distribution with a mean of 17 with standard deviation of 8. What is the probability that for a group of 10 students, the mean number of times they go to the movies each year is between 14 and 18 times?

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53.84% probability that for a group of 10 students, the mean number of times they go to the movies each year is between 14 and 18 times.

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit Theorem

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

In this problem, we have that:

$\mu = 17, \sigma = 8, n = 10, s = \frac{8}{\sqrt{10}} = 2.53$

What is the probability that for a group of 10 students, the mean number of times they go to the movies each year is between 14 and 18 times?

This probability is the pvalue of Z when X = 18 subtracted by the pvalue of Z when X = 14. So

X = 18

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

By the Central Limit Theorem

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

$Z = \frac{18 - 17}{2.53}$

Z = 0.4

Z = 0.4 has a pvalue of 0.6554

X = 14

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

$Z = \frac{14 - 17}{2.53}$

Z = -1.19

Z = -1.19 has a pvalue of 0.1170

0.6554 - 0.1170 = 0.5384

53.84% probability that for a group of 10 students, the mean number of times they go to the movies each year is between 14 and 18 times.

Answer from: Quest

all group life insurance is term insurance. actually it is annual renewable term and it is rated on the average age and claims experience of the entire group, which is called "experience rating." remember, this type of insurance has a 31-day grace period and is convertible to whole life upon leaving employment. a contributory group plan requires that both the employer and the employees pay part of the premium. at least 75% of those eligible must participate, so the group is sure to get most of the healthy employees as well as those that are sick.

step-by-step explanation:

Answer from: Quest

the correct answer is c

good luck love

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