CHAPTER 8 LECTURE NOTES EXAMPLE #2: Suppose that a manufacturer of automobile he
ID: 3311526 • Letter: C
Question
CHAPTER 8 LECTURE NOTES EXAMPLE #2: Suppose that a manufacturer of automobile headlights claims that the distribution of the lifetimes of its best headlight has a mean of 54 months and a standard deviation of 6 months. A consumer group decides to check the claim by purchasing sample of 50 of these headlights and subjecting them to tests that determine their lifetimes. Assuming the manufacturer's claim is true, what is the probability that the consumer group's sample has a mean lifetime of 52 or fewer months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules. ANSWER: 92Explanation / Answer
Mean is 54 and s is 6
for sample of 50, the standard error is SE=s/sqrt(N)=6/sqrt(50)=0.8485
z is given as (x-mean)/SE
thus P(x<52)=P(z<(52-54)/0.8485)=P(z<-2.36) or 1-P(z<2.36)
from normal distribution table we get 1-0.9909 which is 0.0091