# Probability, Confidence INterval

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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.

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

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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 = ...

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