# statics & probability, 4 problems

**Question description**

(17,18,20) Use t-distribution where t**he **population standard deviation,**σ**, is not known. you are given the sample mean and the sample standard deviation. In problem 21 use the standard normal distribution, note the critical value for "tc" depends on the sample size of n.

17. commute time: In a random sample of 8 people, the mean time to commute to work was 35.5 mins and the (sample) standard deviation time was 7.2 minutes. find the margin of error and construct the 95% confidence interval.

18. driving distance: in a random sample of 5 people, the mean driving distance to work was 22.2 miles and the (sample) standard deviation distance was 5.8 miles. find the margin of errorand construct the 95% confidence interval.

20. computer repairs: in a random sampling of seven computer repairs, the mean repair cost was $110.00 and the (sample) standard deviation was $44.50. find the margin of errorand construct the 95% confidence interval.

21. #17 revised (commute time) : after reaserching commute times, you find that the population standard deviation time is actually 9.3 minutes. repet 17 using the standard normal tables with appropriate calculations(not from the t-distribution) and compare problem 17.

please explain guys thanks :)

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