Question

Historical data show that customers who download music from a popular Web service spend approximately​ $24 per​ month, with a standard deviation of ​$3. Assume the spending follows the normal probability distribution. Find the probability that a customer will spend at least ​$20 per month. How much​ (or more) do the top 7​% of customers spend?

What is the probability that a customer will spend at least ​$20 per​ month?

How much do the top 7​% of customers​ spend?

Answer 1

We are given the distribution here as:

a) The probability that customer will spend at least ​$20 per month is computed here as:

P(X > 20)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9088 is the required probability here.

b) From standard normal tables, we have:
P(Z < 1.476) = 0.93

Therefore, P(Z > 1.476) = 0.07

Therefore the lower limit of the amount to be in top 7% is computed here as:
= Mean + 1.476* Std Dev

= 24 + 1.476*3

= 28.428

therefore 28.428 is the required amount here.