Can someone please help with these 6 questions?

5. The distribution of the lengths of pregnancies in human

beings is roughly bell-shaped with mean 268 days and standard

deviation 7 days. The proportion of pregnancies that last at least

one week, i.e., seven days, longer than the average is about

(a) 0.16 (b) 0.68 (c) 0.84 (d) 0.50 (e) 0.32

6. Francesca is allergic to food additive A and to food additive

B. If 22% of all restaurant dishes contain additive A, 17% contain

additive B, and 8% contain both, then the probability that a

randomly selected dish will contain at least one of the two

additives, hence be inedible for Francesca, is about

(a) 0.39 (b) 0.04 (c) 0.47 (d) 0.31 (e) 0.13

20. In a random sample of 325 former prisoners in North

Carolina, 29% were arrested again within one year. A 90% confidence

interval for the proportion of all North Carolina prisoners who are

arrested again within one year is about:

(a) 0.29 Â± 0.05 (b) 0.29 Â± 0.06 (c) 0.29 Â± 0.03 (d) 0.29 Â± 0.07

(e) 0.29 Â± 0.04

21. In the context of the previous problem, suppose that the

confidence interval obtained is too wide. Making use of the

information provided in that problem, the minimum sample size

required in order to estimate the same population proportion to

within two percentage points, still at 90% confidence, is

about:

(a) 684 (b) 1393 (c) 481 (d) 894 (e) 1108

25. In a test of hypotheses H0 : p = 0.42 versus Ha : p

0.42 at the 1% level of

significance a sample of size 1250 produced = 0.39 and test statistic z =

âˆ’2.149. The p-value (the observed significance) of the test is

about:

(a) 0.39 (b) 0.03 (c) âˆ’2.15 (d) âˆ’0.03 (e) 0.42

26. Knowing that drowsiness on the job significantly affects

productivity, the management of a large manufacturing firm

contemplates instituting an expensive program to encourage

employees to get sufficient sleep at night. To test the efficacy of

the program before a full-scale launch, they count the mean number

of quality control rejections per day of manufactured goods on 60

randomly selected days before the inception of a pilot program,

then count the mean number of quality control rejections per day of

goods on 30 days after its inception. The appropriate formula for

the test statistic in the relevant test of hypotheses is: