Review of our pretest on statistics dealing with normal and binomial distributions and normal approximations of a binomial distribution.

1. (1) The scores on the Applied Math exam are normally distributed with a mean
of 68 and a standard deviation of 14.6. If 8% of the students with the lowest
scores fail, determine the pass mark for this exam.
(a) 45 (b) 47 (c) 50 (d) 53

2. (2) An inspection procedure at a manufacturing plant involves picking thirty
items at random and then accepting the whole lot if at least twenty-five of the
thirty items are in perfect condition. If in reality 85% of the whole lot are
perfect, what is the probability that the lot will be accepted?
(a) 0.186 (b) 0.476 (c) 0.524 (d) 0.667 (e) 0.711

3. (3) Tests indicate that the mean life of an electric light bulb in continuous
operation is 87 hours with a standard deviation of 7.5 hours. Asuming a normal
distribution in a total of 1000 light bulbs, approximately how many light bulbs
will last between 72 and 94.5 hours?

4. (4) A medical researcher measured the body temperature of 700 people and
found that the temperatures were normally distributed with a mean of 36.8°C
and a standard deviation of 0.35°C. What is the number of people expected to
have a body temperature of 37.5°C or lower?

5. (5) As part of its yearly plan, a
recreation centre surveyed its
community and gathered the
following data. A frequency
distribution of the number of
children under 18 years of age from 100 families selected at random is shown
above.
(a) Calculate the mean and standard deviation for the number of children in
each family. (2 marks)
(b) What is the probability of a family having from 2 to 4 children under 18 years
of age? (2 marks)
(c) Recalculate the answer to part (b) using a normal approximation of the
binomial distribution. (2 marks)
(d) Why are the answers to part (b) and part (c) slightly different? (2 marks)

6. (5) As part of its yearly plan, a
recreation centre surveyed its
community and gathered the
following data. A frequency
distribution of the number of
children under 18 years of age from 100 families selected at random is shown
above.
(a) Calculate the mean and standard deviation for the number of children in
each family. (2 marks)
(b) What is the probability of a family having from 2 to 4 children under 18 years
of age? (2 marks)

7. (5) As part of its yearly plan, a
recreation centre surveyed its
community and gathered the
following data. A frequency
distribution of the number of
children under 18 years of age from 100 families selected at random is shown
above.
(c) Recalculate the answer to part (b) using a normal approximation of the
binomial distribution. (2 marks)
(d) Why are the answers to part (b) and part (c) slightly different? (2 marks)