Math 10 Exam 1 questions:

(NOTE ANSWER NEED TO BE CORRECT AND PLS SHOW WORK---- NO EXCEPTION)

Question 1

A random variable X has a mean of 655 and a standard deviation of 16. By Chebyshev's theorem, the probability that X will be between 623 and 687 is at least A.) 96%

B.) 88.9%

C.) 75%

D.) 80%

E.) 93.75%

Question 2

A sample of 4 different space heaters is randomly selected from a storage compartment containing 10 that are defective and 31 that have no defects. What is the probability that at least one of the heaters is defective? A.) 0.100

B.) 0.673

C.) 0.689

D.) 0.696

E.) 0.311

Question 3

Use the binomial distribution to find the probability of getting 25 heads in 50 tosses of a fair coin.

A.) 22%

B.) 11%

C.) 50%

D.) 9%

E.) 15%

Question 4

A marketing strategy is effective in 65% of cases. If 3 cases are selected at random, what is the probability that the strategy was not effective in at least one case?

A.) 72.5%

B.) 95.7%

C.) 27.5%

D.) 4.3%

E.) 35.0%

Question 5

What is the probability of getting all heads or all tails in four tosses of a fair coin?

A.) 0.125

B.) 0.015625

C.) 0.0625

D.) 0.25

E.) 0.03125

Question 6

A pair of dice is rolled. Find the probability of rolling an odd sum given that a sum less than 7 is rolled.

A.) 55%

B.) 40%

C.) 60%

D.) 50%

E.) 45%

Question 7

Five cards are drawn from a deck of 52 cards without replacement. Find the probability that three of the cards drawn are not red cards (i.e., hearts or diamonds).

A.) 0.8824

B.) 0.9185

C.) 0.1176

D.) 0.6749

E.) 0.3251

Question 8

A person pays $3 to draw a card. If a card numbered 2 through 10 is drawn, the player wins $1. If a jack or queen is drawn, the player wins $3. If a king or an ace is drawn, the player wins $10. What is the expected value of this game?

A.) -$0.47

B.) -$0.31

C.) -$2.69

D.) -$1.39

E.) -$0.25

Question 9

The table below shows the strategy preferences of 280 tier ranked competitors.

	Tier 1	Tier 2	Tier 3
Alpha strategy	35	35	45
Beta strategy	20	40	25
Gamma strategy	25	20	35

If one of the 280 competitors is randomly selected, find the probability that the person prefers the Gamma strategy or is ranked in Tier 1.

A.) 0.571

B.) 0.286

C.) 0.482

D.) 0.313

E.) 0.455

Question 10

There are 33 Bertie Bott's Every Flavour Beans in a bowl, of which 12 are green, 13 are blue, and 8 are orange. You randomly select one bean, eat it, and then select a second bean. Find the probability that the first bean is orange and the second is green.

A.) 8/99

B.) 1/11

C.) 2/23

D.) 1/132

E.) 32/363

Question 11

How many distinct arrangements of the letters in the word "sleeplessness" are possible?

A.) 6,227,020,800

B.) 12,972,960

C.) 1,081,080

D.) 2,162,160

E.) 155,675,520

Question 12

Use the binomial distribution to determine the standard deviation of the number of aces drawn in 1000 draws with replacement from a deck of 52 cards.

A.) 71.0

B.) 8.4

C.) 76.9

D.) 8.8

E.) 4.4

Question 13

A company with 80 employees has 55 with a PPO insurance plan and 25 with an HMO insurance plan. A sample of 15 empoyees is randomly selected from the company. Find the probability that the sample consists of 9 employees with a PPO plan and 6 employees with an HMO plan.

A.) 0.170

B.) 0.180

C.) 0.185

D.) 0.165

E.) 0.175

Question 14

The table below summarizes the results of a consumer marketing survey for a new sport drink.

	Consumer likes the sport drink	Consumer does not like the sport drink
Consumer is male	61	97
Consumer is female	89	72

A survey participant is randomly selected. What is the probability the consumer is male given that the consumer does not like the sport drink?

A.) 0.495

B.) 0.614

C.) 0.574

D.) 0.304

E.) 0.530

Question 15

A pair of dice is rolled. What is the probability of rolling a sum of 2, 4, 6, or 8?

A.) 0.361

B.) 0.444

C.) 0.333

D.) 0.389

E.) 0.417

Question 16

A recent poll found that 26% of customers surveyed have tried the online reservation service. If 5 customers are selected at random, what is the probability that all 5 have not tried the online reservation service?

A.) 0.222

B.) 0.778

C.) 0.001

D.) 0.999

E.) 0.740

Question 17

A vintage California license plate consists of three letters followed by three numbers. How many such plates are possible if repetitions are not allowed?

A.) 11,232,000

B.) 30,844,800

C.) 46,656,000

D.) 45,239,040

E.) 17,576,000

Question 18

The number of cups of coffee a customer drinks with a meal has the following probability distribution. Find the standard deviation of X.

X	0	1	2	3	4
P(X)	0.29	0.37	0.25	0.04	0.05

A.) 1.11

B.) 1.06

C.) 2.53

D.) 1.59

E.) 1.19

Question 19

The number of cups of coffee a customer drinks with a meal has the following probability distribution. Find the mean of X.

X	0	1	2	3	4
P(X)	0.29	0.37	0.25	0.04	0.05

A.) 1.06

B.) 1.11

C.) 2.53

D.) 1.19

E.) 1.59

Question 20

A regular six-sided die is rolled 2000 times. Use the binomial distribution to determine the expected number of times a value larger than two is rolled. Round your answer to the nearest whole number.

A.) 333

B.) 667

C.) 1667

D.) 1250

E.) 1333