Question

8.A manufacturing company of light bulb claims that an average light bulb lasts 500 days. A contractor randomly selects 30 bulbs for testing. The sampled bulbs last an average of 490 days, with a standard deviation of 100 days. If the claim were true, what is the probability that 30 randomly selected bulbs would have an average life of no more than 490 days?

Answer 1

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The t distribution parameters are given as:

Mean = 500
Xbar = 490
Stdev= 100
n = 30

We will these parameters along with the standardization formula to solve the problem. The formula for standardization is : Z = (X-Mean)/(Stdev/sqrt(n))

We have been asked to find p-value =
P(X<490), let standardize using above formula
= P(t< (490-500)/(100/sqrt(30)))
= -0.5477

So, we have bee nasked to get the p-value

p-value = P(t<-.5477 at df = 30-1 =29) = 0.2940 [look up at t-table or use Excel formula = T.DIST(-.5477,29,TRUE)]

Answer: 0.2940