# Stats Help Suppose You Are Working With A Data Set That Is Normally Distributed

Original question

Stats help Suppose you are working with a data set that is normally distributed, with a mean of 300 and a standard deviation of 44. Determine the value of *x* from the following information.

Round your answers and *z* values to 2 decimal places.

**(a) **70% of the values are greater than *x*

**(b) ***x* is less than 13% of the values.

**(c) **25% of the values are less than *x*

**(d) ***x* is greater than 52% of the values.

According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $175 per hour.

Round the value of *z* to 2 decimal places.

**(a)** At what operating cost would only 20% of the operating costs be less?

**(b)** At what operating cost would 65% of the operating costs be more?

**(c)** What operating cost would be more than 85% of operating costs?

in a recent year, the average price of a Microsoft Windows Upgrade was $90.28 according to *PC Data.* Assume that prices of the Microsoft Windows Upgrade that year were normally distributed, with a standard deviation of $8.53. If a retailer of computer software was randomly selected that year:

Round the values of *z* to 2 decimal places. Round your answers to 4 decimal places, the tolerance is +/-0.0001.

**(a) **What is the probability that the price of a Microsoft Windows Upgrade was below $80?

**(b) **What is the probability that the price was above $95?

**(c) **What is the probability that the price was between $83 and $87?

According to a report by Scarborough Research, the average monthly household cellular phone bill is $60. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.35.

**(a)** What is the probability that a randomly selected monthly cell phone bill is more than $85?

**(b)** What is the probability that a randomly selected monthly cell phone bill is between $45 and $70?

**(c)** What is the probability that a randomly selected monthly cell phone bill is between $65 and $75?

**(d)** What is the probability that a randomly selected monthly cell phone bill is no more than $40?

Round the values of z to 2 decimal places. Round your answers to 4 decimal places, the tolerance is +/-0.0001.

**(a)**

*P*(*x* > 85) =

**(b)**

*P*(45 < *x* < 70) =

**(c)**

*P*(65 < *x* < 75) =

**(d)**

*P*(*x* ≤ 40) =

Tompkins Associates reports that the mean clear height for a Class A warehouse in the United States is 22 feet. Suppose clear heights are normally distributed and that the standard deviation is 5 feet. A Class A warehouse in the United States is randomly selected.

**(a)** What is the probability that the clear height is greater than 17 feet?

**(b)** What is the probability that the clear height is less than 13 feet?

**(c)** What is the probability that the clear height is between 26 and 32 feet?

Round the values of z to 2 decimal places.Round your answers to 4 decimal places.

**(a)**

P(x > 17) =

**(b)**

P(x < 13) =

**(c)**

P(26 ≤ x ≤ 32) =

AND THEN IF YOU WOULDN’T MIND SHOWING WORK FOR A COUPLE OF THESE PROBLEM BELOW I JUST WAN TO GET A BETTER IDEA OF HOW TO CALCULATE I DON’T KNOW IF I have to use the probability table or not.

Determine the probabilities for the following normal distribution problems.

Round the values of z to 2 decimal places.Round your answers to 4 decimal places.

**(a)** *μ* = 604, *σ* = 56.8, *x* ≤ 635:

**(b)** *μ* = 48, *σ* = 12, *x* < 20:

**(c)** *μ* = 111, *σ* = 33.8, 100 ≤ *x* < 150:

**(d)** *μ* = 264, *σ* = 10.9, 250 < *x* < 255:

**(e)** *μ* = 37, *σ* = 4.35, *x* > 35:

**(f)** *μ* = 156, *σ* = 11.4, *x* ≥ 170: