Question

The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. All probabilities should be to four decimal places.

What is the probability that a randomly selected computer will have a price of at least $1,530? Answer

Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount? (Round to two decimal places) Answer

What are the minimum and the maximum values of the middle 95% of computer prices? (Round to two decimal places) Minimum Answer, Maximum

Answer 1

Solution :

Given that ,

mean = = 1200

standard deviation = = 220

(a)

P(x 1530) = 1 - P(x   1530)

= 1 - P((x - ) / (1530 - 1200) / 220)

= 1 -  P(z 1.5)  

= 1 - 0.9332

= 0.0668

Probability = 0.0668

(b)

P(x > 1750) = 1 - P(x < 1750)

= 1 - P((x - ) / < (1750 - 1200) / 220)

= 1 - P(z < 2.5)

= 1 - 0.9938

= 0.0062

Probability = 0.0062

(c)

The middle 95% has the z values are : -1.96 and +1.96

x = z * +

x = -1.96 * 220+ 1200 = 768.8

x = 1.96 * 220 + 1200 = 1631.2

Minimum value = 768.8

Maximum value = 1631.2