12.     In a study of the lifetimes 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.

b.    About 95% of the sample components had life- times between 306.3 and 433.7 hours.

c.    If someone takes a random sample of 400 components, divides the sample standard deviation of their lifetimes by 20, and then adds and sub- tracts that quantity from the sample mean, there is about a 68% chance that the interval so con- structed will cover the mean lifetime of this type of component.

d.    The z table can’t be used to construct confidence intervals here, because the lifetimes of the compo-

ii.    one-fourth as wide

iii.    one-half as wide

iv.    the same width

v.    twice as wide

vi.    four times as wide

vii.     eight times as wide