Question

Historical data show that customers who download music from a popular Web service spend approximately $22 per month, with a standard deviation of $3. Find the probability that a customer will spend at least $20 per month. How much (or more) do the top 10 percent of customers spend?

Answer 1

Solution :

Given that,

mean = = 22

standard deviation = = 3

P(x >20 ) = 1 - P(x< 20)

= 1 - P[(x -) / < (20-22) /3 ]

= 1 - P(z <-0.67 )

Using z table

= 1 -  0.2514

probability= 0.7486

b

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z ) = 1 - 0.10

= P(Z < z ) = 0.9

z = 1.28 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.28 *3+22

x=25.84=26 rounded