1. Replacement times for TV sets are normally distributed with a mean of 8.2 yea

Question

1. Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.2 years ( based on data from "Gettings things fixed," Consumer Reports.)

A) If a TV is randomly selected, find the probability its replacement time is greater than 10 years. Is the result unusual? Explain.

B) Find the probability that a randomly selected TV will have a replacement time between 9 years and 12 years.

C) If you want to provide a warranty so that only 2% (lower 2%) of the TV sets will be replaced before the waranty expires, what is the time length of then warranty?

Explanation / Answer

Solution:

From the given information = 8.2 and = 1.2 we have:
a) P(X > 10 ) = P(X/>108.2/1.2)
= P (Z>1.5) = 0.0668

b) P(9 < X < 12) = P(98.2/1.2 < X/ < 128.2/1.2)
= P(0.67 < Z < 3.17) = 0.2506

c) Find z so that P(z) = 0.02.
z = -2.0538
x-8.2/1.2 = -2.0538
x-8.2 = -2.4645
x = 5.7354 yrs

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.