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Probability, Confidence INterval

Please show all work.

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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