In a study of the lifetime of electronic components, a random sample of 400 comp

Question

In a study of the lifetime of electronic components, a random sample of 400 components
are tested until they fail to function. The sample mean lifetime was 370 hours and the
standard deviation was 650 hours. True or false:
a. An approximate 95% confidence interval for the mean lifetime of this type of
component is from 306.3 to 433.7 hours. (3 points)
b. About 95% of the sample components had lifetimes between 306.3 and 433.7
hours. (3 points)
c. If someone takes a random sample of 400 components, divides the sample
standard deviation of their lifetimes by 20, and then adds and subtracts that
quantity from the sample mean, there is about a 68% chance that the interval so
constructed will cover the mean lifetime of this type of component. (3 points)
d. The z table can’t be used to construct the confidence intervals here, because the
lifetimes of the components don’t follow the normal curve.

Explanation / Answer

Ans:

Sampling distribution of sample means follow normal distribution irrespective of the population distribution,when sample size is large.

Given that

mean=370

standard deviation=650

sample size,n=400

standard error of mean=650/sqrt(400)=32.5

95% confidence interval for mean

=370+/-1.96*32.5

=370+/-63.7

=(306.3, 433.7)

Option a is true.

(others are not true)

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