MCQ 17-24 practice

A teacher has a box of 48 pens. The following table shows the classification of all 48 pens in the box by whether they are ballpoint or fountain pens and whether they are red or blue. One pen from the box will be selected at random. Based on the table, which of the following statements is correct?

• The probability of selecting a red pen is greater than the probability of selecting a blue pen.

• The probability of selecting a fountain pen is less than the probability of selecting a ballpoint pen.

• The probability of selecting a red pen is greater than the probability of selecting a ballpoint pen.

• The probability of selecting a red pen given that the pen is a ballpoint pen is less than the probability of selecting a red pen given that the pen is a fountain pen.

• The probability of selecting a ballpoint pen given that the pen is red is greater than the probability of selecting a ballpoint pen given that the pen is blue.

Tags

CCSS.HSS.CP.B.6

Chan commutes to work by using a ride-share service to the train station and then taking a train to his office. From experience, he estimates the probability that he is delayed using the ride-share service is 0.4. The train service reports that the probability of a train delay is 0.25 and this result (delay or not) is independent of the ride-share service result (delay or not). What is the probability that Chan will be delayed by at least one of his two modes of transport on a randomly selected commute to work?

• 0.10

• 0.15

• 0.30

• 0.45

• 0.55

Tags

CCSS.HSS.CP.B.7

A local convenience store purchases a certain type of candy in bulk from a large distributor. The probability distribution of the number of candies purchased is shown in the table. The convenience store pays the distributor $0.25 per candy. What is the expected cost of the candy purchase for the convenience store?

• $11.63

• $45.00

• $90.00

• $46.50

• $186.00

Tags

CCSS.HSS.MD.A.2

Parvez’s parents measure his height against the wall using uncooked spaghetti noodles. The average length of one uncooked spaghetti noodle is 27.5 centimeters with a standard deviation of 0.83 centimeters. Parvez stands with his feet on the ground and back to the wall. His parents place the first spaghetti noodle directly above a 10-centimeter baseboard, then stack additional noodles one on top of another until they reach the top of Parvez’s head. For the most recent measurement, Parvez measured exactly 7 spaghetti noodles tall. Assuming the lengths of spaghetti noodles are independent, what is the standard deviation of the total height for 7 randomly selected spaghetti noodles stacked on top of the baseboard to measure Parvez’s height?

• 10 + √(7×(0.83)²)

• 10 + 7²(0.83)²

• √(7(0.83)²)

• √(72(0.83)²)

• √(102 + 7(0.83)²)

On a very large Spotify playlist, 5% of the songs are by Mariana’s favorite artist. She plans to listen to the playlist on shuffle, which plays the songs in a random order with replacement. What is the probability that the first song by her favorite artist is the eighth song she listens to from the playlist?

• 1 – (0.05)^8

Tags

CCSS.8.EE.C.8C

Approximately 70% of people in the United States watched at least some of the most recent Olympic Games. Consider two separate random samples selected from the U.S. population: one with 75 people and the other with 150 people. Which of the following statements is true regarding the probability that less than 60% of the sample watched at least some of the most recent Olympic games?

• It is less likely for a sample of 75 people, because there is less variability in the sampling distribution for smaller sample sizes.

• It is less likely for a sample of 150 people, because there is less variability in the sampling distribution for larger sample sizes.

• It is less likely for a sample of 75 people, because there is more variability in the sampling distribution for smaller sample sizes.

• It is less likely for a sample of 150 people, because there is more variability in the sampling distribution for larger sample sizes.

• They are equally likely, because the sample proportion is an unbiased estimator of the population proportion.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

LinkedIn is a popular professional networking site and claims that approximately 60% of their accounts belong to Millennials, the generation of people born between 1981 and 1996. Suppose a simple random sample of 40 LinkedIn accounts is selected and three-quarters of the accounts in the sample belong to Millennials. A LinkedIn employee wonders if this provides convincing statistical evidence that more than 60% of LinkedIn accounts belong to Millennials. A random number generator is used to simulate the selection of 40 LinkedIn accounts from a population in which 60% of the accounts belong to Millennials. The dotplot shows the percentage of Millennial accounts in 250 trials of this simulation. Based on the results of the simulation, what conclusion should the LinkedIn employee draw?

• A) Because most of the simulated sample percentages fall between 55% and 60%, there is not convincing statistical evidence that more than 60% of accounts on LinkedIn belong to Millennials.

• B) Only 6/250, or 2.4%, of simulated sample percentages are greater than or equal to 75%, which does provide convincing statistical evidence that more than 60% of the accounts on LinkedIn belong to Millennials.

• C) Only 6/250, or 2.4%, of simulated sample percentages are greater than or equal to 75%, so it is unlikely that more than 60% of the accounts belong to Millennials.

• D) About half of the simulated sample percentages are greater than or equal to 60%, which provides convincing statistical evidence that more than 60% of the accounts on LinkedIn belong to Millennials.

• E) About half of the simulated sample percentages are greater than or equal to 60%, which does not provide convincing statistical evidence that 60% of the accounts on LinkedIn belong to Millennials.

Tags

CCSS.7.SP.A.2

A pontoon boat has a weight limit of 2,500 pounds and the manufacturer claims that it can safely hold 14 people. If the weights of adult females are approximately normally distributed with μ = 170 pounds and σ = 24.5 pounds, which of the following is the approximate probability that a random sample of 14 adult females will be able to safely ride on the pontoon boat.

• 0.001

• 0.095

• 0.500

• 0.905

• 0.999

Tags

CCSS.HSS.ID.A.4