Barb
secondary (10-12)
student
The question is this one:
Replacement times for TV sets are normally distributed with a mean of
8.2 years and a standard deviation of 1.1 years. Estimate the probability
that for 250 randomly selected TV sets, at least 15 of them have replacement
times greater than 10.0 years.
Thank you for your reply. I have been battling this problem for 2 days.
Hi Barb,
Use the normal distribution to find the probability that a single TV set would have a replacement time of greater than 10.0 years.
Pr(10.0 < X) = Pr( (10.0 - 8.2)/1.1 < Z) = Pr(1.64 < Z)
which is approximately 0.05.
Now you have a binomial problem. You have a random sample
of n = 250 TV sets, "success" is a TV set with replacement time of greater
than 10.0 years, so p = 0.05 and you want the probability of
at least 15 successes. Since n is large you should use the normal approximation
to the binomial. Thus the number of successes X has, approximately,
a normal distribution with mean np = 250 
0.05 = 12.5
and variance np(1-p) and you want the probability that X is larger than
15.
Can you see how to complete the problem now?
Andrei and Penny