Problem Set

1.         Determine the area under the standard normal curve that lies

a.         to the left of Z = –2.01

b.         to the right of Z = 1.97.

c.         between Z = –2.31 and Z = 0.

d.         between Z = –2.01 and Z = 1.07.

e.         between Z = 1.47 and Z = 2.31.

f.          between Z = –3.11 and Z = 1.47.

g.         to the left of Z = –3.31 or to the right of Z = 2.40.

2.         The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. The Department of Molecular Genetics at Ohio State University requires a GRE score no less than the 75th percentile. (Source: www.biosci.ohio-state.edu/~molgen/html/admission_criteria.html.)

a.         Find the Z-score corresponding to the 75th percentile. In other words, find the Z-score such that the area under the standard normal curve to the left is 0.75.

b.         How many standard deviations above the mean is the 75th percentile?

3.         The diameters of ball bearings produced at a factory are approximately normally distributed. Suppose the mean diameter is 1.02 centimeters (cm) and the standard deviation is 0.02 cm. The product specifications require that the diameter of each ball bearing be between 0.98 and 1.02 cm.

a.         What proportion of ball bearings can be expected to have a diameter under 1.00 cm?

b.         What proportion of ball bearings can be expected to have a diameter over 1.00 cm?

c.         What proportion of ball bearings can be expected to have a diameter between 0.98 and 1.02 cm? That is, what proportion of ball bearings can be expected to meet the specifications?

d.         What is the probability that the diameter of a randomly selected ball bearing will be over 0.96 cm?

e.         What is the probability that the diameter of a randomly selected ball bearing will be under 0.995 cm?

f.          What is the percentile rank of a ball bearing that has a diameter of 0.99 cm?

g.         What is the percentile rank of a ball bearing that has a diameter of 1.01 cm?

h.         Determine the 10th percentile of the diameters of ball bearings.

i.          Determine the diameters of ball bearings that make up the middle 99% of all diameters.

• 5 years ago
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