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Probability Questions 3A

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1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 68% of all pregnancies last between
a. 250 and 282 days b. 234 and 298 days c. 218 and 314 days d. 250 and 266 days

2. The distribution of actual weights of chocolate bars produced by a certain machine is approximately Normal with mean 8.2 ounces and standard deviation of 0.1 ounces. What proportion of chocolate bars weigh under 8 ounces?
a. 13.5% b. 34% c. 16% d. 2.5%

3. Sixteen weighings of a small object on a sensitive scale result in 5.15 grams 4 times, 5.35 grams 4 times, 5.20 grams, 4 times and 5.30 grams 4 times, 16 total. If the standard deviation σ of weighings on this scale is .8 grams, what is an approximate 95% confidence interval for the true weight of the object?
a. 5.25 ±.4 b. 5.25 ±.2 c. 5.25 ±.8 d. 5.20 ±.2

4. A survey of 900 gun-owners who frequent a popular shooting range in Texas had a nearly 100% response rate. If only 18% of the respondents thought more laws on gun control should be enacted, the conclusion that less than 20% of people in the region support more gun laws would certainly be dubious due to which of the following?
a. large standard deviation of samples of size 900 b. nonresponse from the sample
c. sampling bias of respondents d. small sample size

5. Scores on a test for 8th graders range from 0 to 500. In a SRS of 400 students, the mean score is 335 and the standard deviation is 70. The standard deviation of the sampling distribution of x̅400 is what?
a. 70/335 b. 400/70 c. 70/20 d. 335/20

6.The weights of a sample of 400 2-year-olds in Kentucky yields x̅400 is 21.2 pounds with a standard deviation of σ = 3 pounds. What is a 95% confidence interval for the weight of all two-year-olds in Kentucky?
a. 18.2-21.5 pounds b. 15.2-27.2 pounds c. 21.185-22.015 pounds d. 20.9-21.5 pounds
7.When finding confidence intervals, the interval is smaller if
a.sample size and standard deviation are bigger b.sample size and standard deviation are smaller
c.sample size is bigger, but the standard deviation is smaller d.sample size is smaller, but standard deviation is bigger.

8. If the birth weights of the babies born annually in a hospital is Normal with a mean of 5 pounds 10 ounces and a standard deviation of 5 ounces, what percentage of babies are born weighing less than 5 pounds? (No table needed.)
a. 13.5% b. 2.5% c. 16% d. .3%

9. What percent of the babies born weigh between 5 pounds and 5 pound 5 ounces? (Again no table.)
a. 13.5% b. 47.5% c. 16% d. 34%

10. Of the 40 babies born during the first weeks of next month, how many are likely to be under five pounds?
a. 4 b. 2 c. 6 d. 1

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1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 68% of all pregnancies last between
a. 250 and 282 days b. 234 and 298 days c. 218 and 314 days d. 250 and 266 days

Use the empirical rule with 1 standard deviation.
266 - 16 = 250
266 + 16 = 282

2. The distribution of actual weights of chocolate bars produced by a certain machine is approximately Normal with mean 8.2 ounces and standard deviation of 0.1 ounces. What proportion of chocolate bars weigh under 8 ounces?
a. 13.5% b. 34% c. 16% d. 2.5%

8.2 - 2*0.1 = 8
By the empirical rule with 2 standard deviations, the answer is 2.5%.

3. Sixteen weighings of a small object on a sensitive scale result in 5.15 grams 4 times, 5.35 grams 4 times, 5.20 grams, 4 times and 5.30 grams 4 times, 16 total. If the standard deviation σ of ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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