STAT 200, FINAL (CHAPTERS 6-12)
EXAM QUESTIONS AND ANSWERS
GRADED A+ 2025/2026
What's wrong with the following statement?: "because the digits 0, 1, 2, ..... , 9 are the normal
results from lottery drawings, such randomly selected numbers have a normal distribution." -
ANS since the probability of each digit being selected is equal, lottery digits have a uniform
distribution, not a normal distribution.
a normal distribution is informally described as a probability distribution that is "bell-shaped"
when graphed. draw a rough sketch of a curve having the bell shape that is characteristic of a
normal distribution - ANS looks like a rollercoaster, incline at the bottom that goes into an
upside-down u-shape.
what requirements are necessary for a normal probability distribution to be a standard normal
probability distribution? - ANS the mean and standard deviation have the values of µ = 0 and
σ=1
what does the notation z subscript α indicate? - ANS the expression z subscript α denotes the
z score with an area of α to its right
the waiting time between a subway departure schedule and the arrival of a passenger are
uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected
passenger has a waiting time greater then 3.25 minutes - ANS 0.458
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
,the waiting time between a subway departure schedule and the arrival of a passenger are
uniformly distributed between 0 and 5 minutes. find the probability that a randomly selected
passenger has a waiting time less then 3.75 minutes - ANS 0.75
find the area of the shaded region. the graph depicts the standard normal distribution with
mean 0 and standard deviation 1. z= 0.95 and the graph is shaded to the left - ANS the area
of the shaded region is 0.8289
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the left, is 0.3015 - ANS the indicated
z score is -0.52
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the right, is 0.8708 - ANS the
indicated z score is -1.13
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the right, is 0.2061 - ANS the
indicated z score is 0.82
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a
given score is less that -1.81 and draw a sketch of the region - ANS the probability is 0.0351.
the sketch is bell-shaped with the area to the left shaded at the -1.81 mark, to show that it is
less than -1.81
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a
given score is less than 2.23 and draw a sketch of the region - ANS the sketch is bell-shaped
with the area to the left shaded at the 2.23 mark, to show that it is less than 2.23
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the
probability of a bone density test score greater than -1.78. - ANS the sketch is bell-shaped
with the area to the right shaded at the -1.78 mark, to show that it is greater than -1.78
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the
probability of a bone density score between -1.66 and 1.66. - ANS the sketch is bell-shaped
with the area between -1.66 and 1.66 shaded to show that it is between -1.66 and 1.66
find the indicated critical value of z subscript 0.07 - ANS 1.48
about _______% of the area is between z=-1 and z=1 (or within 1 standard deviation of the
mean) - ANS 68.27%
about _______% of the area is between z=-2 and z=2 (or within 2 standard deviations of the
mean) - ANS 95.45%
about _____% of the area is between z=-3 and z=3 (or within 3 standard deviations of the
mean) - ANS 99.75%
which of the following is not a descriptor of a normal distribution of a random variable?
a. the graph of the distribution is bell-shaped
b. the graph is centered around the mean
c. the graph is centered around 0
d. the graph of the distribution is symmetric - ANS c. the graph is centered around 0
A continuous random variable has a _____ distribution if its values are spread evenly over the
range of possibilities - ANS uniform
which of the following is not a requirement for a density curve?
a. every point on the curve must have a vertical height that is 0 or greater
b. the graph is centered around 0
c. the curve cannot fall below the horizontal axis
3 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
EXAM QUESTIONS AND ANSWERS
GRADED A+ 2025/2026
What's wrong with the following statement?: "because the digits 0, 1, 2, ..... , 9 are the normal
results from lottery drawings, such randomly selected numbers have a normal distribution." -
ANS since the probability of each digit being selected is equal, lottery digits have a uniform
distribution, not a normal distribution.
a normal distribution is informally described as a probability distribution that is "bell-shaped"
when graphed. draw a rough sketch of a curve having the bell shape that is characteristic of a
normal distribution - ANS looks like a rollercoaster, incline at the bottom that goes into an
upside-down u-shape.
what requirements are necessary for a normal probability distribution to be a standard normal
probability distribution? - ANS the mean and standard deviation have the values of µ = 0 and
σ=1
what does the notation z subscript α indicate? - ANS the expression z subscript α denotes the
z score with an area of α to its right
the waiting time between a subway departure schedule and the arrival of a passenger are
uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected
passenger has a waiting time greater then 3.25 minutes - ANS 0.458
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
,the waiting time between a subway departure schedule and the arrival of a passenger are
uniformly distributed between 0 and 5 minutes. find the probability that a randomly selected
passenger has a waiting time less then 3.75 minutes - ANS 0.75
find the area of the shaded region. the graph depicts the standard normal distribution with
mean 0 and standard deviation 1. z= 0.95 and the graph is shaded to the left - ANS the area
of the shaded region is 0.8289
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the left, is 0.3015 - ANS the indicated
z score is -0.52
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the right, is 0.8708 - ANS the
indicated z score is -1.13
find the indicated z score. the graph depicts the standard normal distribution with mean 0 and
standard deviation 1. the area of the shaded region, to the right, is 0.2061 - ANS the
indicated z score is 0.82
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a
given score is less that -1.81 and draw a sketch of the region - ANS the probability is 0.0351.
the sketch is bell-shaped with the area to the left shaded at the -1.81 mark, to show that it is
less than -1.81
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. find the probability that a
given score is less than 2.23 and draw a sketch of the region - ANS the sketch is bell-shaped
with the area to the left shaded at the 2.23 mark, to show that it is less than 2.23
assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the
probability of a bone density test score greater than -1.78. - ANS the sketch is bell-shaped
with the area to the right shaded at the -1.78 mark, to show that it is greater than -1.78
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, assume that a randomly selected subject is given a bone density test. those test scores are
normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the
probability of a bone density score between -1.66 and 1.66. - ANS the sketch is bell-shaped
with the area between -1.66 and 1.66 shaded to show that it is between -1.66 and 1.66
find the indicated critical value of z subscript 0.07 - ANS 1.48
about _______% of the area is between z=-1 and z=1 (or within 1 standard deviation of the
mean) - ANS 68.27%
about _______% of the area is between z=-2 and z=2 (or within 2 standard deviations of the
mean) - ANS 95.45%
about _____% of the area is between z=-3 and z=3 (or within 3 standard deviations of the
mean) - ANS 99.75%
which of the following is not a descriptor of a normal distribution of a random variable?
a. the graph of the distribution is bell-shaped
b. the graph is centered around the mean
c. the graph is centered around 0
d. the graph of the distribution is symmetric - ANS c. the graph is centered around 0
A continuous random variable has a _____ distribution if its values are spread evenly over the
range of possibilities - ANS uniform
which of the following is not a requirement for a density curve?
a. every point on the curve must have a vertical height that is 0 or greater
b. the graph is centered around 0
c. the curve cannot fall below the horizontal axis
3 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
