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# Probability, Confidence INterval

1. Suppose the salary of assembly line workers has Normal distribution with mean of \$20,000, and standard deviation of \$3,000.

a) What is the probability that a randomly selected assembly line worker earns more than \$22,000?

b) What is the probability that the average salary of 5 assembly line workers is higher than \$22,000?

c) What is the probability that the average salary of 15 assembly line workers is higher than \$22,000?

2. Our client asked us to compute a 97% confidence interval for the time it takes to build a house in Kamloops. There are 32 observations in our sample. The sample mean is 60 days.

a) What is the 99% confidence interval, if the population standard deviation is known to be 10 days?

b) What is the 99% confidence interval, if the sample standard deviation is 10 days

c) Find the 80% confidence interval, if the population standard deviation is known to be 10 days.

#### Solution Preview

The solution file is attached.

1. Suppose the salary of assembly line workers has Normal distribution with mean of \$20,000, and standard deviation of \$3,000.
a) What is the probability that a randomly selected assembly line worker earns more than \$22,000? (2 marks)
b) What is the probability that the average salary of 5 assembly line workers is higher than \$22,000? (2 marks)
c) What is the probability that the average salary of 15 assembly line workers is higher than \$22,000? (2 marks)

(a)
μ = 20000
σ = 3000
x = 22000
z = (x - μ)/σ = 0.666667
P(x > \$22000) = 0.2525

(b)
μ = ...

#### Solution Summary

The Solutions provide the required probabilities for Question 1 and Confidence intervals in respect of Question 2.

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