Question

1. Customers at the local Subway store order an ice tea with their meal 70% of the time. Use the Binomial distribution to find the answer to the following.

Find the probability that among the next 8 customers, at least 3 will order ice tea with their meal:  (to three places after the decimal)

Of the next 8 customers, how many do you expect to order ice tea with their meal?  (to one place after the decimal)

2. The average score of all golfers for a particular course has a mean of 66 and a standard deviation of 5.

Find the mean of the sampling distribution for the average score (sample mean) of 196 golfers:  (Round answer to the nearest integer.)


Find the standard deviation of the sampling distribution for the average score (sample mean)of 196 golfers:   (Round answer to four places after the decimal.)

Is the sampling distribution of the average score (sample mean) approximately normal?

a) Yes, because the sample size is large enough.

b) No, because the sample size is not large enough.     

What is the probability that the average (sample mean) of the 196 golfers exceeded 67?   (Round answer to four places after the decimal.)

What is the standard deviation of the number of customers that order ice tea among the next 8 customers?  (to two places after the decimal)

3. We are interested in estimating the proportion of people that can identify Nebraska but not Vermont. In a class of 55 students, each student was requested to select a sample of 6 people, show each person a map of the US and ask the person to identify the states of Vermont and Nebraska. The following numbers are the counts that each student got, that is, each number is the count of people in the student sample of 6, that could identify Nebraska but not Vermont.  

4
4
5
5
0
1
0
1
1
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0


Note: You can cut and past these numbers into an excel spreadsheet to help you calculate the mean and the standard deviation and compute the confidence interval. If you have trouble pasting them, paste them to a text file first and then copy from there.

When we collect all the students' data, we have a sample size of 6x55=330.

Of the sample of 330 people, what proportion were able to locate Nebraska but not Vermont?  

Find a 95% confidence interval for the true proportion of people that can locate Nebraska but not Vermont. The 95% confidence interval is ( ,   ).  
(Round answers to two places after the decimal.)

Answer 1

We would be looking at question 1 all parts here.

Question 1:

The number of people who orders ice tea along with their meal is given by a distribution here as:

a) Probability that of the 8 customers,  at least 3 will order ice tea with their meal is computed using binomial distribution function here as:

Therefore 0.9887 is the required probability here.

b) Number of customers expected to order ice tea with their meal out of the next 8 customers is computed here as:

= 8*0.7

= 5.6

Therefore 5.6 is the expected number of customers here.