MA116 -- More Problems for Chapter 3
Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard
deviation of 15 oz.
1. The proportion of infants with birth weights above 125 oz is
a. 0.500 * b. 0.159 c. 0.341 d. 0.841.
2. The proportion of infants with birth weights between 125 oz and 140 oz is
a. 0.819 b. 0.636 c. 0.477 * d. 0.136
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The scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15.
3. The proportion of adults with scores between 90 and 110 is closest to
a. 0.250 b. 0.432 * c. 0.500 d. 0.667
4. The proportion of adults with scores above 130 is closest to
a. 0.001 * b. 0.025 c. 0.050 d. 0.950
5. How high a score is needed to be in the highest 5%?
a. 115 * b. 124 c. 130 d. 135
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A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of soap powder in such a box has a Normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight.
6. What proportion of boxes is underweight (i.e., weigh less than 32 oz)?
* a. 0.0764 b.0 .2420 c. 0.7580 d. 0.9236
7. How heavy does a box have to be for it to be labeled overweight?
a. 31.60 oz b. 31.85 oz * c. 34.15 oz d. 34.40 oz
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A market research company employs a large number of typists to enter data into a computer database. The time taken for new typists to learn the computer system is known to have a Normal distribution with a mean of 130 minutes and a standard deviation of 20 minutes. A candidate is automatically hired if he or she learns the computer system in less than 100 minutes. A cut-off time is set at the slowest 40% of the learning distribution. Anyone slower than this cut-off time is not hired.
8. The proportion of new typists that take under two hours to learn the computer system is
a. 0.023 b. 0.067 c. 0.159 * d. 0.309
9. What proportion of candidates will be automatically hired?
a. 0.023 * b. 0.067 c. 0.159 d. 0.309
10. What is the cut-off time the market research company uses?
a. 2 hours and 8 minutes * b. 2 hours and 14 minutes
c. 2 hours and 30 minutes d. 2 hours and 40 minutes
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Scores on the SAT verbal test in recent years follow approximately the N(504,111) distribution.
11. The proportion of students scoring under 400 is
a. 0.044 b. 0.095 * c. 0.174 d. 0.956
12. The proportion of students scoring between 450 and 550 is
a. 0.517 b. 0.436 * c. 0.347 d. 0.248
13. How high must a student score to place in the top 10% of all students taking the SAT?
a. 598 b. 615 * c. 647 d. 687
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14. The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded passing grade?
a. 62 b. 57 * c. 44 d. 40
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15. The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so 80% of the students will complete the exam in the time given?
a. 84 minutes * b. 78.4 minutes c. 92.8 minutes d. 79.8 minutes
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16. The time taken for a computer link to be made between the terminal in an executive’s office and the computer at a remote factory site has a Normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions, the computer link is made in less than
a. 19.39 seconds b. 15.95 seconds c. 11.16 seconds * d. 18.84 seconds
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17. A soft drink machine can be regulated so it discharges an average of μ oz per cup. If the ounces of fill are Normally distributed, with a standard deviation of 0.4 oz, what value should μ be set at so 6-oz cups will overflow only 2% of the time?
a. 6.82 b. 6.00 * c. 5.18 d. 5.60