AP Stats Chapter 16 Practice

In a particular game, a fair die is tossed.  If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing.  Let X be the amount that you win. 
Which of the following is the expected value of X?

• $1.00
• $2.50
• $4.00
• $6.00

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day.  Based on the records, X has the following probability distribution.
The mean number of customers that make a purchase during the first hour that the store is open is:
   

• 2.0
• 2.5
• 2.9
• 3

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is

• .1056
• .3944
• .1042
• .8944

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once.
What is the expected value of Z?

• 1.7
• 4.4
• 5.8
• 11.6

Your friend Albert has invented a game involving two ten-sided dice.  One of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens.  He won’t tell you how many of each number there are on the faces, but he does tell you that if X = the result of a single roll of the first die and Y = the result of a single roll of the second die, then μ_x=3.6, σ_x=0.8, μ_y=8.0 and σ_y=0.9. Let Z = the sum of the two dice when each is rolled once. 
Here's Albert's game: You give him $10 each time you roll, and he pays you (in dollars) the amount that comes up on the dice.  If P = the amount of money you gain each time you roll, the mean and standard deviation of P are:

• μ_P=-1.6; σ_P=1.45
• μ_P=1.6; σ_P=1.45
• μ_P=1.6; σ_P=1.2
• μ_P=-1.6; σ_P=13.8

Mike's job is just a few bus stops away from his house.  While it can be faster to take the bus to work, it’s more variable, because of variations in traffic.  He estimates that the commute time to work by bus is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 4 minutes.  The commute time if he walks to work is also approximately Normally distributed with a mean of 16 minutes with a standard deviation of 1 minute.  What is the probability that the bus will be faster than walking?

• .8340
• .8485
• .8980
• .9756

In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes are independent, which of the following represents the probability that you win at least once?

• (0.2)⁵
• 1-(0.2)⁵
• 1-(0.8)⁵
• (₅C₂)(0.2)(0.8)⁴

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise.  What is the expected amount you win?

• $0.00
• -$1.00
• $1.00
• $3.00

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

The mean amount of time to mix the batter for a cake is 14 minutes with a standard deviation of 2.5 minutes. The mean amount of time to bake the cake is 35 minutes with a standard deviation of 6.2 minutes. What is the mean time to make and bake a cake? What is the standard deviation?

• mean = 49 min sd = 8.7 min

• mean = 49 min sd = 6.685 min

• mean = 21 min sd = 8.7 min

• mean = 21 min sd = 6.685 min

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.ID.A.2

The mean hourly salary for a high school graduate is $13.50 per hour with a standard deviation of $5.75. The mean hourly salary for a person with an Associate's degree is $19.75 with a standard deviation of $9.25. What is expected difference in the hourly salaries between a high school graduate and a person who earned an Associate's degree?

• $33.25

• $-3.50

• $-6.25

• $15.00

Tags

CCSS.8.EE.C.8C