## 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:___

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2021-09-15T06:05:56+00:00
2021-09-15T06:05:56+00:00 1 Answer
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## Answers ( )

Answer:(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 salaryThe 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 =

0.3446The 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 salaryThe 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 =

0.078The above probability is calculated by looking at the value of x = 1.42 in the z table which has an area of 0.9222.