Download AP Review Continuous Dist MC

Name: ______________________________________________
AP Statistics
5) Consider the following two normal curves:
AP Review – Continuous Distributions #1
1) If 75% of all families spend more than $75 weekly for food, while
15% spend more than $150, what is the mean weekly expenditure and
what is the standard deviation? Assume a normal distribution.
a) μ = 83.33, σ = 12.44
d) μ = 104.39, σ = 43.86
b) μ = 56.26, σ = 11.85
e) μ = 139.45, σ = 83.33
c) μ = 118.52, σ = 56.26
2) The income per household in a certain state is normally distributed
with a mean $9500 and a standard deviation of $1750. The middle
95% of incomes are between what two values?
a) $5422 and $13,578
d) $7260 and $11,740
b) $6070 and $12,930
e) $8049 and $10,951
c) $6621 and $12,379
3) The noise level in a restaurant is normally distributed with an
average of 30 decibels and a standard deviation of 4 decibels. Ninetynine percent of the time it is below what value?
a) 20.7
d) 37.8
b) 32.0
e) 39.3
c) 33.4
4) An electronic product takes an average of 3.4 hours to move
through an assembly line. If the time is normally distributed with a
standard deviation of 0.5 hour, what is the probability that an item will
take between 3 and 4 hours to go through the line?
a) .2119
d) .3811
b) .2295
e) .6730
c) .3270
a
b
Which has the larger mean and which has the larger standard
deviation?
a) Larger mean a; larger standard deviation a
b) Larger mean a; larger standard deviation b
c) Larger mean b; larger standard deviation a
d) Larger mean b; larger standard deviation b
e) Larger mean b; same standard deviation
6) Which of the following statements is false?
a) In all normal distributions, the mean and the median are equal.
b) All bell-shaped curves are normal distributions for some μ and σ.
c) Virtually all the area under a normal curve is within three standard
deviations, no matter what the particular μ and σ are.
d) For all normal curves, there is approximately a 95% chance that an
observation will be within 2 standard deviations of the mean.
e) The fiftieth percentile of a normal distribution is the mean of the
distribution.
7) A z-score is called a standardized score because you can
a) translate any x-value into a z-score.
b) translate any x-value from a normal distribution into a z-score.
c) translate z-scores into a proportion, a percentile, or a probability of
the normal curve.
d) use z-scores to find the area between a z-score and the mean, or the
area below a z-score.
e) use them to compare x-values to a universal standard, in this case,
the standard normal distribution.
8) Suppose the grades on the last AB Calculus quiz are uniformly
distributed with a range of 46 and a median of 72. What is the
probability that a randomly selected student did not pass?
a) .4565
d) .5
b) .5435
e) 1.52
c) .9130
12) Which of the following is the least likely to fit a normal
distribution?
a) Distribution of heights of professional soccer players
b) Distribution of the weights of salmon in the Pacific Ocean
c) Distribution of test scores among those who took the SAT in 2003
d) Distribution of the ages of automobiles in drivable condition
e) Distribution of the points scored by a basketball player per game
9) Which of the following is true about the areas described under the
normal curve?
a) The area below the mean is greater than the area above the mean.
b) The area in the range from z = 0 to z = 1 is the same as the area in
the range from z = 1 to z = 2.
c) Roughly 50% of the observations are located at the mean of the
distribution.
d) Fewer than 1% of the observations are three standard deviations
above or below the mean.
e) 95% of the observations have values twice that of the mean.
13) You have two normally distributed populations:
Population A: μ = 50 and σ= 12
Population B: μ = 75 and σ = 15
Which of the following has the greatest area?
a) Area below 25 in Population A
b) Area above 65 in Population A
c) Area between 75 and 90 in Population B
d) Area below 60 in Population B
e) Area above 80 in Population B
10) Suppose the density curve at the right
represents the GPAs of AHS students, what
is the probability that a randomly selected
student will have a GPA over 2.5?
a) .5
d) .75
b) .625
e) .25
c) .375
14) All the following would be evidence that you do not have a normal
distribution, except
a) the presence of multiple modes.
b) the fact that 75% of the observations have a value below the mean.
c) a normal probability plot suggests an obviously curved line.
d) the likelihood for all values of x is the same.
e) None of the above.
.3
.2
.1
1
2
3
4
5
11) Which of the following statements about a uniform distribution is
false?
a) The area below the mean is greater than the area above the mean.
b) The area in the range from z = 0 to z = 1 is the same as the area in
the range from z = 1 to z = 2.
c) The mean and median are always equal.
d) If the range is 10, then the minimum x-value is located 5 units
below the mean.
e) The height of the distribution is calculated using 1/range.
15) Assume that a baseball team has an average pitcher, that is, one
whose probability of winning any game is .5. If this pitcher has 30
games in a season, what is the probability that he will win at least 20
games?
a) .0505
d) .3333
b) .2514
e) .4300
c) .2743