Elementary Statistics Exam 3 Questions with Solutions
1. Left-handedness occurs in about 12% of all Americans. Males are slightly more
likely than females to be left-handed, with 13% of males and 11% of females being left-
handed. Suppose a random sample of 80 females and 100 males is chosen.
Let X be the number of males (out of the 100) who are left-handed. Let Y be
the number of females (out of the 80) who are left-handed.
Let Z be the total number of left-handed individuals in the sample (males and females
together).
Which of the following is true regarding the random variables X and Y?: Only X can be
well approximated by a normal random variable.
2. Suppose the scores on an exam are normally distributed with a mean ¼= 75 points
and standard deviation Ã= 8 points.
What is the exam score for an exam whose z-score is 1.25?: 85
3. The score of golfers for a particular course follows a normal distribution that has a
mean of 73 and a standard deviation of 3. Suppose a golfer played the course today.
Find the probability that her score is at least 74.: 0.3694
4. Suppose the scores on an exam are normally distributed with a mean ¼= 75 points,
and standard deviation Ã= 8 points.
1
, Suppose that the top 4% of the exams will be given an A+. In order to be given an A+,
an exam must earn at least what score? Report your answer in whole numbers.: 89
5. The following histogram displays the distribution of battery life (in hours) for a
certain battery model used in cell phones:
Suppose that battery life is a normal random variable with ¼= 8 and Ã= 1.2. Using the
Standard Deviation Rule, how likely is it that a randomly chosen battery lasts longer
than 10.4 hours?: 0.16
6. The number of days (X) after mailout it takes a utility company to receive payment
for a customer's bill is a normal random variable with a mean of 31 days and a
standard deviation of 6 days
The probability is 0.997 and that bill will be received between which of the following
number of days?: (13,49)
7. According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a
social worker was 28.08 with a standard deviation of 1.97. Veronica
is a social worker with an hourly wage of 31.60. What is Veronica's z-score? (Round
your answer to 2 decimal places): 1.79
8. The time it takes a surgeon to complete a laproscopic surgery to remove the gall
bladder is normally distributed with a mean of 132.4 minutes and
a standard deviation of 15.7 minutes. A patient's risk of complications is increased the
longer he is in surgery. An unusually risky surgery is one that is in the top 4% of all
2
1. Left-handedness occurs in about 12% of all Americans. Males are slightly more
likely than females to be left-handed, with 13% of males and 11% of females being left-
handed. Suppose a random sample of 80 females and 100 males is chosen.
Let X be the number of males (out of the 100) who are left-handed. Let Y be
the number of females (out of the 80) who are left-handed.
Let Z be the total number of left-handed individuals in the sample (males and females
together).
Which of the following is true regarding the random variables X and Y?: Only X can be
well approximated by a normal random variable.
2. Suppose the scores on an exam are normally distributed with a mean ¼= 75 points
and standard deviation Ã= 8 points.
What is the exam score for an exam whose z-score is 1.25?: 85
3. The score of golfers for a particular course follows a normal distribution that has a
mean of 73 and a standard deviation of 3. Suppose a golfer played the course today.
Find the probability that her score is at least 74.: 0.3694
4. Suppose the scores on an exam are normally distributed with a mean ¼= 75 points,
and standard deviation Ã= 8 points.
1
, Suppose that the top 4% of the exams will be given an A+. In order to be given an A+,
an exam must earn at least what score? Report your answer in whole numbers.: 89
5. The following histogram displays the distribution of battery life (in hours) for a
certain battery model used in cell phones:
Suppose that battery life is a normal random variable with ¼= 8 and Ã= 1.2. Using the
Standard Deviation Rule, how likely is it that a randomly chosen battery lasts longer
than 10.4 hours?: 0.16
6. The number of days (X) after mailout it takes a utility company to receive payment
for a customer's bill is a normal random variable with a mean of 31 days and a
standard deviation of 6 days
The probability is 0.997 and that bill will be received between which of the following
number of days?: (13,49)
7. According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a
social worker was 28.08 with a standard deviation of 1.97. Veronica
is a social worker with an hourly wage of 31.60. What is Veronica's z-score? (Round
your answer to 2 decimal places): 1.79
8. The time it takes a surgeon to complete a laproscopic surgery to remove the gall
bladder is normally distributed with a mean of 132.4 minutes and
a standard deviation of 15.7 minutes. A patient's risk of complications is increased the
longer he is in surgery. An unusually risky surgery is one that is in the top 4% of all
2
