109 Statistics Homework
1. A firm manufactures light bulbs that have a life, before burn-out, that is normally
distributed with mean equal to 800 hours and a stand deviation of 40 hours. Find the
probability that a bulb burns between 778 and 834 hours.
2. Gauges are used to reject all components for which a certain dimension is not within the
specification 1.50  d. It is known that this measurement is normally distributed with
mean 1.50 and standard deviation 0.2. Determine the value d such that the specification
“cover” 95% of the measurements.
3. A chemical engineer claims that the population mean yield of a certain batch process is
500 grams per milliliter of raw material. To check this claim the engineer samples 25
batches each month. The engineer is hoping for a significance level (α) of 10%. What
conclusion should the engineer draw from a sample that has a mean 𝑥̅ = 518 grams per
milliliter and a sample standard deviation s=40 g/ml? Does this sample fall within the
appropriate confidence interval? Assume the distribution of yield to be approximately
normal.
4. An instructor plans to assess the math skills of students before and after an engineering
course. A math test was given at the beginning of the semester, and the same test was
given again at the end of the semester. The scores are shown in the table (out of 100
maximum score).
Student # 1
2
3
4
5
6
7
8
9
Before
61
58
79
69
53
71
48
25
62
After
68
62
83
65
51
74
52
31
62
(a) Are students’ math skills improved? (use 95% CI)
(b) Test at the 5% level of significant if the students’ math skills improved.