# 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.