Can someone please help with these 6 questions? 5. The distribution of the lengt
ID: 3314993 • Letter: C
Question
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 ± 0.05 (b) 0.29 ± 0.06 (c) 0.29 ± 0.03 (d) 0.29 ± 0.07 (e) 0.29 ± 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
(a) 0.39 (b) 0.03 (c) 2.15 (d) 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:
Explanation / Answer
5)P(X>268+7)=P(Z>7/7)=P(Z>1)=0.16 option A (a) 0.16
6)probability that a randomly selected dish will contain at least one of the two additives =0.22+0.17-0.08=0.31
option d
20) sample proportion p=0.29
for n=325 ; std error =(p*(1-p)/n)1/2 =0.0252
for 90% CI ; crtiical z =1.645
therefore 90% confidence interval =p -/+ z*std errror =0.29-/+0.04
option E
21)
margin of error E =0.02
for 90% CI ; critical z =1.645
p=0.29
therefore required sample size n=p(1-p)*(Z/E)2 =1393
option B
25)
herefor abive test statistic p value =0.0316
option B