Question

[5]       3.   The average teacher’s salary is $45,000. Assume a normal distribution with standard

                  deviation equal to $10,000.

1. What is the probability that a randomly selected teacher makes greater than $65,000 a year?

2. If we sample 100 teachers’ salaries, what is the probability that the sample mean will be greater than $65,000?

Answer 1

Mean = = 45000

Standard deviation = = 10000

a) We have to find P(X > 65000)

For finding this probability we have to find z score.

That is we have to find P(Z > 2)

P(Z > 2) = 1 - P(Z < 2) = 1 - 0.9772 = 0.0228 ( Using z table)

b)

Sample size = n = 100

We have to find P( > 65000)

For finding this probability we have to find z score.

That is we have to find P(Z > 20)

P(Z > 20) = 1 - P(Z < 20) = 1 - 1 = 0.0000