An automobile club comes to the aid of stranded motorists who are members. Over the long run, about 6% of the members utilize this service in any 12-month period. A small town has 400 members of the club. Consider the 400 members to be representative of the larger club membership. Let p̂ be the proportion of them who will utilize the service in the coming 12-month period. (a) Explain how the following conditions for the approximate normality of the sampling distribution for a sample proportion are met in this scenario. State any assumptions that you need to make to do so. The Physical Situation: Either there is an actual population with a fixed proportion who have a trait or opinion of interest, or there is a repeatable situation for which an outcome of interest occurs with a fixed relative frequency probability. (Select all that apply.) There is an actual population with a fixed proportion who have a trait or opinion of interest.There is a repeatable situation for which an outcome of interest occurs with a fixed relative frequency probability. Data Collection: Either a random sample is selected from an actual population, or the situation is repeated numerous times, with the outcome each time independent of outcomes all other times. (Select all that apply.) A random sample is selected from an actual population.The situation is repeated numerous times, with the outcome each time independent of outcomes all other times. Sample Size or Number of Trials: The size of the sample or number of binomial trials must be large enough that we expect to see at least ten of each of the two possible responses or outcomes. That is, np and n(1 − p) must each be at least 10. np = 24 n(1 − p)= 376 (b) What are the values of n and p in this situation? n=.06 p=400 (c) Describe the sampling distribution of p̂, including values for the mean and standard deviation. (Round your answer for the standard deviation to four decimal places.) The mean is___.06_ . The standard deviation is__.0119__ . (d) 1)The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? 2)What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)

An automobile club comes to the aid of stranded motorists who are members. Over the long run, about 6% of the members utilize this service in any 12-month period. A small town has 400 members of the...

An automobile club comes to the aid of stranded motorists who are members. Over the long run, about 6% of the members utilize this service in any 12-month period. A small town has 400 members of the club. Consider the 400 members to be representative of the larger club membership. Let p̂ be the proportion of them who will utilize the service in the coming 12-month period.

(a)

Explain how the following conditions for the approximate normality of the sampling distribution for a sample proportion are met in this scenario. State any assumptions that you need to make to do so.

The Physical Situation: Either there is an actual population with a fixed proportion who have a trait or opinion of interest, or there is a repeatable situation for which an outcome of interest occurs with a fixed relative frequency probability. (Select all that apply.)

There is an actual population with a fixed proportion who have a trait or opinion of interest.There is a repeatable situation for which an outcome of interest occurs with a fixed relative frequency probability.

Data Collection: Either a random sample is selected from an actual population, or the situation is repeated numerous times, with the outcome each time independent of outcomes all other times. (Select all that apply.)

A random sample is selected from an actual population.The situation is repeated numerous times, with the outcome each time independent of outcomes all other times.

Sample Size or Number of Trials: The size of the sample or number of binomial trials must be large enough that we expect to see at least ten of each of the two possible responses or outcomes. That is,
np

and
n(1 − p)

must each be at least 10.

np = 24

n(1 − p)= 376

(b)

What are the values of
n
and
p
in this situation?

n=.06

p=400

(c)

Describe the sampling distribution of p̂, including values for the mean and standard deviation. (Round your answer for the standard deviation to four decimal places.)

The mean is___.06_ . The standard deviation is__.0119__ .

(d)

1)The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town?

2)What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)

Jun 09, 2022

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An automobile club comes to the aid of stranded motorists who are members. Over the long run, about 6% of the members utilize this service in any 12-month period. A small town has 400 members of the...

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