## g The average teachers salary in north Dakota is $37,764. Assume a normal distribution with LaTeX: \sigma=\text{5100}σ = 5100. a) For a samp Question g The average teachers salary in north Dakota is$37,764. Assume a normal distribution with LaTeX: \sigma=\text{5100}σ = 5100. a) For a sample of 75 teachers, what is the probability that the mean is greater than $38,000? Present your answer in 4 decimal places. b) What is the probability that a randomly selected teacher’s salary is grater than$45,000? Present your answer in three decimal places. Present your answers as: a:___,b:___

in progress 0
4 weeks 2021-09-15T06:05:56+00:00 1 Answer 0

(a) Probability that the mean is greater than $38,000 is 0.3446. (b) Probability that a randomly selected teacher’s salary is grater than$45,000 is 0.078.

Step-by-step explanation:

We are given that the average teachers salary in north Dakota is $37,764. Assume a normal distribution with sigma (σ) = 5100. (a) A sample of 75 teachers is taken. Let = sample mean salary The z score probability distribution for sample mean is given by; Z = ~ N(0,1) where, = population mean salary =$37,764

= standard deviation = $5,100 n = sample of teachers = 75 Now, probability that the mean is greater than$38,000 is given by = P( > $38,000) P( >$38,000) = P( > ) = P(Z > 0.40) = 1 – P(Z < 0.40)

= 1 – 0.6554 = 0.3446

The above probability is calculated by looking at the value of x = 0.40 in the z table which has an area of 0.6554.

(b) Let X = a randomly selected teacher’s salary

The z score probability distribution for normal distribution is given by;

Z  =    ~ N(0,1)

where, = population mean salary = $37,764 = standard deviation =$5,100

Now, probability that a randomly selected teacher’s salary is grater than $45,000 is given by = P(X >$45,000)

P(X > \$45,000) = P( > ) = P(Z > 1.42) = 1 – P(Z < 1.42)

= 1 – 0.9222 = 0.078

The above probability is calculated by looking at the value of x = 1.42 in the z table which has an area of 0.9222.