Question

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1000 and the standard deviation is $135. Round answers to at least 4 decimal places, use technology.

1)What is the probability that a buyer paid between $865 and $1135?

2)What is the probability that a buyer paid between $1000 and $1270?

3)What price would the buyer pay to get 9% the most expensive HD televisions?

Answer 1

Solution :

1)

P($865 < x < $1135) = P[(865 - 1000)/ 135) < (x - ) /  < (1135 - 1000) / 135) ]

= P(-1 < z < 1)

= P(z < 1) - P(z < -1)

= 0.8413 - 0.1587

= 0.6826

Probability = 0.6826

2)

P($1000 < x < $1270) = P[(1000 - 1000)/ 135) < (x - ) /  < (1270 - 1000) / 135) ]

= P(0 < z < 2)

= P(z < 2) - P(z < 0)

= 0.9772 0.5

= 0.4772

Probablity = 0.4772

3)

Using standard normal table ,

P(Z < z) = 9%

P(Z < -1.34) = 0.09

z = -1.34

Using z-score formula,

x = z * +

x = -1.34 * 135 + 1000 = 819.1

819.1 price would the buyer pay to get 9% the most expensive HD televisions.