The average price of a television on a certain Web site is $820. Assume the pric

Question

The average price of a television on a certain Web site is $820. Assume the price of these televisions follows the normal distribution with a standard deviation of $170. Complete pads a through d below. What is the probability that a randomly selected television from the site sells for less than $700?.2420 (Round to four decimal places as needed.) What is the probability that a randomly selected television from the site sells for between $400 and $500? (Round to four decimal places as needed.) What is the probability that a randomly selected television from the site sells for between $900 and $1,000? (Round to four decimal places as needed.) There are 17 televisions on the site. How many televisions are within a $800 budget? There are televisions on the site that are within a $800 budget. (Round down to the nearest whole number.)

Explanation / Answer

Params of the normal distribution are given in the question. I am listing it down below:

Mean = 820

Stdev = 170

We will use Z tables to solve the questions:

a. P(X<700) = P(Z< 700-820 / 170) = P(Z<-.71) = .2389

b. P( 400<X<500) = P( -2.47<Z<-1.88) = .0301-.0068 = .0233

c. P(900<X<1000) = P(.47<Z<1.06) =.8554- .6808 = .1746

d. P(X<800) = P(Z< 800-820 / 170) = .4562
So, since there are 17 TV in total: .4562*17 = 7.75 or 8 TVs

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