multiple choice
essay
mixed questions
100
Which of the following is a continuous random variable?
a) H= number of Hats sold Tuesday
b) P = number of points scored by Stephen Curry in a game
c) X = number of incoming flights at the local airport
d) T = winning time in men's 100-meter dash at the 2016 Olympics
d) T = winning time in men's 100-meter dash at the 2016 Olympics
100
Identify if the following scenarios describe a discrete or continuous random variable.
Explain your choice.
(a) X = The number of persons in an emergency room
(b) W = The weights of delivery trucks at a supermarket.
(c) H = The areas of houses being built in a new subdivision.
(a) Discrete. X could take any of the integer values 0, 1, 2, ..., N but not values like 21.5.
(b) Continuous. W could take many positive values.
(c) Continuous. H could take many positive values.
100
Estimate the mean and standard deviation of the normal density curve in the figure.
Mean = ________
Standard deviation = __________
Mean = 15
Standard Deviation = 3
200
A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428 ?
a) 95%
b) 99.7%
c) 68%
d) 34%
c) 68%
200
Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let X = the number of free throws Faith makes out of 20 shots.
(a) Explain why X is a binomial random variable.
(b) Calculate the mean of X.
(c) Calculate the standard deviation of X.
(d) Use the binomial probability formula to find P(X=19). Interpret this value in context.
(e) Her coach says that he will let the team out of practice early if Faith makes 18 or more free throws. What is the probability that practice ends early? Show your work.
(a) Binary? “Success” = made free throw “Failure” = missed free throw
a. Independent? Knowing whether or not a free throw is made does not affect the probability of making another free throw.
b. Number? n = 20.
c. Same probability? p = 0.95.
(b) μx = 20(0.95) = 19
(c) σx = �20(.95)(0.05) = 0.975
(d) P(X=19) = 20C19(0.95)19(0.05)1 = 0.377, There is a 0.377 probability of Faith making exactly 19 out of 20 free throws.
(e) P(X ≥ 18) = 20C18(0.95)18(0.05)2 + 20C19(0.95)19(0.05)1 + 20C20(0.95)20(0.05)0= 0.9245
200
It is known that 15% of the seniors in a large high school enter military service upon graduation. If a group of 20 seniors are randomly selected, what is the probability of observing two who will be entering military service?
a) 20C18(0.15)^18(0.85)^2
b) 20C2(0.15)^18(0.85)^2
c) 20C2(0.15)^2(0.85)^18
d) 20C2(0.15)^2(0.85)^20
c) 20C2(0.15)^2(0.85)^18
300
Twenty percent of all trucks undergoing a certain inspection will fail the inspection. Assume that 40 trucks are independently undergoing inspection, one at a time. The expected number of trucks who fail the inspection is?
a) 16
b) 8
c) 40
d) 20
b)8
300
A researcher has a colony of bongo spiders in his lab. There are 1200 adult spiders in the colony, and their weights are normally distributed with a mean of 11 grams and a standard deviation of 2 grams.
(a) Sketch a normal curve and label the axis using the mean and standard deviation. Be sure to label one, two, and three standard deviations on either side of the mean.
(b) Using the 68-95-99.7 rule, about what percent of spiders in the colony weigh between 7 grams and 13 grams?
(c) Using the 68-95-99.7 rule, about what percent of spiders in the colony weigh less than 9 grams?
(d) Approximately 68% of all the spider weights would occur between what two weight values?
(e) What is the z-score of a spider in this colony that weighs 15 grams?
(f) What percent of spiders in the colony weigh more than 15 grams?
a)
(b) 81.5%
(c) 16%
(d) Approximately 68% of all the spider weights would occur between 9 grams and 13 grams.
(e) z = 15−11/2 = 2
(f) 2.5%
300
Which of the following is not a condition for the binomial setting?
(a) The trials are independent.
(b) There are two possible outcomes for each trial, which we can classify as a success or failure.
(c) In any set of n trials, there is at least one success.
(d) There are a fixed number of trials of a random process.
(c) In any set of n trials, there is at least one success.
400
Which of the following is the closest to z-score to the 90th percentile of the standard and normal distribution?
a) 2.36
b) 1.28
c) - 1.28
d)- 1.34
b)1.28
400
A manufacturing company has designed a new test of mechanical aptitude for its machinists. Scores on this test can be approximated with a Normal distribution with μ=400 and σ = 60. What score would a machinist need in order to be in the top 10% of all machinists who would take this test?
400 + 60(1.28) = 476.8
400
In a certain large lake 30% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake.
Let Y = the number of fish that you throwback because they are too small.
(a) Explain how Y can be considered a binomial random variable.
(b) Find the probability that exactly 5 fish are thrown back. Show your work.
(c) Calculate and interpret the mean of Y.
(d) Calculate and interpret the standard deviation of Y.
(a) Binary? “Success” = fish is thrown back “Failure” = fish is not thrown back
a. Independent? Knowing whether or not a fish is thrown back does not affect the probability of another fish being thrown back.
b. Number? n = 20.
c. Same probability? p = 0.30.
(b) P(Y=5) = 20C5(0.30)5(0.70)15 = 0.1789
(c) μx = 20(0.30) = 6 If we catch many, many samples of 20 fish we expect to throw back 6 fish, on average.
(d) σx = �20(0.30)(0.70) = 2.049 We expect the number of fish thrown back out of 20 will typically vary by 2.049 fish from the mean of 6 fish.
500
If the foot length of women follows a normal distribution with a mean of 23 cm, and 81.5% have a foot length between 20 cm and 29 cm, what is your estimate of the standard deviation of the heights in this population?
a) 2.25 cm
b) 9 cm
c) 4.5 cm
d) 3 cm
d) 3cm
500
A bookstore has determined that weekly sales of a pop culture magazine can be modeled by an approximately Normal distribution with a mean of 75 copies and a standard deviation of 6 copies.
a) For what percentage of the weeks can the store expect to sell between 70 and 85 copies of the magazine?
b) For what percentage of the weeks can the store expect to sell less than 66 magazines?
c) If the bookstore stocks 86 copies of the magazine, what percentage of weeks will Is there an insufficient number of copies to meet demand?
(a) 74.99%
(b) 6.68%
(c) 3.34%
500
The proportion of pepperoni pizza orders on a randomly selected day at a local pizza shop is approximately normal with mean 0.25 and standard deviation 0.02. Let X = the proportion of pepperoni pizza orders on a randomly selected day.
(a) Carefully sketch a normal curve for this situation. Be sure to label the mean and one, two, and three standard deviations on each side of the mean.
Use the 68–95–99.7 rule to approximate:
(b) P(X > 0.29)
(c) The probability that the proportion of pepperoni pizza orders is between 0.21 and 0.27.
Use Table A to answer the following:
(d) What is the probability that the proportion of pepperoni pizza orders is between 0.24 and
0.28?
(e) What is the probability that the proportion of pepperoni pizza orders is greater than 0.30?
a)
(b) 0.025
(c) 0.815
(d) 0.9332 - 0.3085 = 0.6247
(e) 1 - 0.9938 = 0.0062