# Determine the probabilities for the following normal distribution

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:

(c) μ = 111, σ = 33.8, 100 ≤ x < 150:

(d) μ = 264, σ = 10.9, 250 < x < 255:

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?

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.