A population contains seven million 0s and eight million 1s. What is the sampling distribution of the sample mean when the sample size is n=5?

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Part 1

Let X be the number of 1s. Complete the chart below.

X	P(X)	x
0
1
2
3
4
5

2) Given a population with a mean of =104 and a variance of 2=49, the central limit theorem applies when the sample size is n25. A random sample of size n=25 is obtained.

a. What are the mean and variance of the sampling distribution for the sample means?

b. What is the probability that x>105?

c. What is the probability that 102

d. What is the probability that x104.5?

Part 1

a. The mean is ____.

Part 2

The variance is _____.

(Round to two decimal places as needed.)

Part 3

b. The probability that x>105 is ____.

(Round to four decimal places as needed.)

Part 4

c. The probability that 102

(Round to four decimal places as needed.)

3) A chain of coffee shops is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and the company wishes to establish a sales monitoring process to identify the shops that are underperforming. Historically the daily mean sales for a shop has been $11,500 with a variance of 4,000,000.

Their monitoring plan will take a random sample of 8 days sales per month and use the sample mean sales to identify shops that are underperforming. Establish the lower limit sales such that only 5% of the shops would have a sample sales mean below this value.

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Part 1

The lower limit would be $_____.

(Round to two decimal places as needed.)