Quiz about Statistics Review 2 (Topics 5 - 7)

Question 1

One hundred and thirty-two individuals were selected at random and asked which brand of car they preferred. They were then sorted by age.

What is the probability that a person, selected at random, is in the 50 - 65 age group or prefers Toyota? Write your answer as a decimal rounded to four places.

Accepted Answer

$$\frac{36}{132}+\frac{56}{132}-\frac{22}{132}\approx0.5303$$

Answer

$$\frac{36}{132}+\frac{56}{132}\approx0.6970$$

Answer

$$\frac{22}{132}\approx0.1667$$

Answer

$$\frac{22}{36}\approx0.6111$$

Answer

$$\frac{22}{56}\approx0.3929$$

Question 2

One hundred and thirty-two individuals were selected at random and asked which brand of car they preferred. They were then sorted by age.

Does there appear to be an association between a person's age and what brand of car they prefer?

Accepted Answer

Yes; A person's age and car brand preference seem to be associated because there is variation in the data.

Answer

No; A person's age and car brand preference are independent.

Question 3

N(0, 1)

Which of the following are properties of a Normal Distribution? Choose all that apply.

Accepted Answer

symmetric

Accepted Answer

bell-shaped

Accepted Answer

unimodal

Answer

positively skewed

Answer

negatively skewed

Question 4

This data is normally distributed. What percent of the data is in the shaded region?

Accepted Answer

95%

Answer

50%

Answer

68%

Answer

99.7%

Question 5

This data is normally distributed. What percent of the data is in the shaded regions?

Accepted Answer

5%

Answer

0.15%

Answer

2.35%

Answer

10%

Answer

0.3%

Question 6

For patients in Dr. Jones' office, blood pressure has a mean of 115 with a standard deviation of 6. What percent of patients have blood pressure below 115?

Accepted Answer

50%

Answer

0%

Answer

25%

Answer

100%

Answer

75%

Question 7

Given a mean test score of 75 and a standard deviation of 7, use the Empirical Rule to find the percentage of scores that are between 75 and 82.

Accepted Answer

34%

Answer

68%

Answer

50%

Answer

25%

Answer

10%

Question 8

The distribution of the annual incomes of a group of employees at Compton Plastics approximates a normal distribution with a mean of $30,000 and a standard deviation of $2000. About 95% of the incomes lie between what two amounts?

Accepted Answer

$26,000 and $34,000

Answer

$27,000 and $33,000

Answer

$28,000 and $36,000

Answer

$30,000 and $34,000

Question 9

95% of students weigh between 62 kg and 90 kg.

Assuming this data is normally distributed, what are the mean and standard deviation?

Accepted Answer

Mean = 76 kg

S.D. = 7 kg

Answer

Mean = 66 kg

S.D. = 7 kg

Answer

Mean = 86 kg

S.D. = 7 kg

Answer

Mean = 76 kg

S.D. = 14 kg

Question 10

Suppose that a normal model describes the annual snowfall in Massachusetts (in inches). Last year's snowfall measurement had a z-score of -2.2. This means that last year the snowfall was

Accepted Answer

2.2 standard deviations below the average

Answer

-2.2 inches total

Answer

2.2 inches less than average

Answer

The snowfall is 1 - .22 inches below the average

Question 11

Jayden scored a 65 on his calculus test, where the class average was 70 and the standard deviation was 10.

Shyann scored a 46 on her algebra quiz, where the class average was 48 and the standard deviation was 3.

Who performed better comparatively on their assessment?

Accepted Answer

Jayden

Answer

Shyann

Question 12

$$X$$ is normally distributed with a mean of 12 and a standard deviation of 8.

Which image corresponds to $$P\left(X>15\right)$$ ?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Question 13

$$N\left(10,\ 5\right)$$

$$P\left(4

Accepted Answer

0.5404

Answer

0.4806

Answer

0.5747

Answer

0.6802

Answer

0.3418

Question 14

Fernando is 60 inches tall. The average height for his age and gender is 68 with a standard deviation of 10 inches. What percent of his peers are shorter than him?

Accepted Answer

21.19%

Answer

46.81%

Answer

8%

Answer

78.81%

Question 15

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. If a dairy product is randomly selected, what is the probability that it will be "spoiled" in 8 days or less?

Accepted Answer

.0912

Answer

.4082

Answer

.5918

Answer

.9082

Question 16

The scores obtained by students on a math test are normally distributed with a mean score of 61 and a standard deviation of 10. Find the probability that a randomly chosen student obtains a score higher than 85.

Accepted Answer

0.0082

Answer

0.4207

Answer

0.1112

Answer

0.9918

Answer

0.1424

Question 17

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What percentage ratings can be expected to be between 200 and 275?

Accepted Answer

43.32%

Answer

56.71%

Answer

38.61%

Answer

29.87%

Question 18

If I tell you that you scored at the 55th percentile on your final exam, you would know:

Accepted Answer

55% of the class scored worse than you did.

Answer

You earned a 55% on the exam.

Answer

You failed the exam.

Answer

45% of the class scored worse than you did.

Answer

55% of the class scored better than you did.

Question 19

At the college level, the jumping distances for male long jumpers are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.
Suppose a male long jumper's jump ranked in the 75th percentile. How long was his jump?

Accepted Answer

272.44 inches

Answer

0.67 inch

Answer

263 inches

Answer

277.25 inches

Question 20

Which four conditions are true for a binomial distribution?

Accepted Answer

The probability of a success (p) must be the same for each event.

Accepted Answer

There can be only two complementary outcomes: success or failure.

Accepted Answer

There is a fixed number of trials (sample size).

Accepted Answer

Each trial must be independent.

Answer

The probability for each event must be 0.5

Question 21

In the following situation, identify n, p, q, and x for the binomial distribution:

A sea turtle's chance at survival is 2%. Counting a nest of 82 sea turtles, what is the probability that exactly 1 will survive?

Accepted Answer

n=82, p=0.02, q=0.98, x=1

Answer

n=1, p=0.02, q=0.98, x=82

Answer

n=82, p=0.98, q=0.02, x=1

Answer

n=1, p=0.98, q=0.02, x=82

Question 22

Bob is taking a 100 question test. They have a 90% probability of getting any one question correct.

Which is the correct formula to find that Bob will answer exactly 70 questions correctly? P(X=70) = ___

$$P\left(x\right)=nCx\cdot p^x\cdot q^{\left(n-x\right)}$$

Accepted Answer

₁₀₀C₇₀ ( 0.90 )⁷⁰ ( 0.10 )³⁰

Answer

₁₀₀C₇₀ ( 0.90 )⁷⁰( 0.10 )⁰

Answer

₁₀₀C₇₀ ( 0.90 )⁶⁰( 0.10 )³⁰

Answer

₉₉C₇₀ ( 0.90 )⁷⁰ ( 0.10 )³⁰

Question 23

In a particular town, the probability that a randomly chosen voter is a Republican is 0.35.

What is the probability that in a sample of 10 voters in the town, at least 1 will be a Republican?

***Complement Shortcut: $$P\left(X\ge1\right)=1-P\left(none\right)$$

Accepted Answer

0.9865

Answer

0.2275

Answer

0.0725

Answer

0.0135

Question 24

An egg supplier to a restaurant sends a daily shipment of 500 eggs. Previous records show that 4% of these eggs arrive damaged to the restaurant. Let X = the number of eggs that arrive damaged on a randomly selected day.

Find the mean (expected value) and standard deviation of X.

$$\mu=np\ \ \ and\ \ \ \ \sigma=\sqrt[]{npq}$$

Accepted Answer

Mean=20

SD = 4.38

Answer

Mean = 2000

SD = 34.6

Answer

Mean = 200

SD = 11.0

Answer

Mean = 2

SD = 1.41

Question 25

An egg supplier to a restaurant sends a daily shipment of 500 eggs. Previous records show that 4% of these eggs arrive damaged to the restaurant. If the average number of damaged eggs is 20, with a standard deviation of 4.38, would it be unusual for 29 damaged eggs to arrive in a daily shipment?

Usual Range: $$-2\le Z\le2$$ or $$\left[\mu-2\sigma,\ \mu+2\sigma\right]$$

Accepted Answer

Yes; 29 is more than 2 standard deviations from the mean.

Answer

Yes; 29 is within 2 standard deviations of the mean.

Answer

No; 29 is more than 2 standard deviations from the mean.

Answer

No; 29 is within 2 standard deviations of the mean.

Question 26

A binomial distribution $$B\left(n,p\right)$$ is approximately normal when the number of successes and the number of failures are both 10 or more ( $$np\ge10$$ and $$nq\ge10$$ ). For which of the binomial distributions listed below is the normal distribution a reasonable approximation?

Accepted Answer

B(50, 0.4)

Answer

B(40, 0.12)

Answer

B(75, 0.11)

Answer

B(40, 0.8)

Question 27

Normal Approximation of a Binomial Distribution:

30% of all dogs in a city are microchipped. In a sample of 500 dogs, what is the probability that less than 140 dogs are microchipped? Select the closest option.

Accepted Answer

16%

Answer

25%

Answer

21%

Answer

13%

Question 28

How many more students liked hockey and baseball combined than basketball?

Accepted Answer

4

Answer

1

Answer

5

Answer

9

Question 29

Which of the following statements are true? [Select all that apply.]

Accepted Answer

From January to March, chocolate sales dropped drastically. They then boomed to 50% in April before decreasing slightly in the last month.

Accepted Answer

From January to May, ice cream sales decreased at a steady rate. Ice cream sales in May were 40% less than what they were in January.

Accepted Answer

From January to May, biscuit sales increased from 40% to 95%. In the last month, buscuit sales were more than double the chocolate sales.

Question 30

What does the x-axis of this bar graph show?

Accepted Answer

Types of Fruit

Answer

Number of People

Question 31

What frequency scale does the bar graph use?

Accepted Answer

5

Answer

1

Answer

2

Answer

10

Question 32

Look at the bar graph and answer the following question:

Which is the most common type of allergy among children 0-4 years old?

Accepted Answer

Skin Allergy

Answer

Respiratory allergy

Answer

Food allergy

Question 33

Look at the bar graph and answer the following question:

What percentage of children between 10-17 years old have a food allergy?

Accepted Answer

5%

Answer

10%

Answer

20%

Question 34

Look at the bar graph and answer the following question:

Which type of allergy is more common among children 5-9 years old?

Accepted Answer

Respiratory allergy

Answer

Food allergy

Answer

Skin Allergy

Question 35

Look at the bar graph and answer the following question:

Which type of allergy shows the smallest difference between age groups?

Accepted Answer

Food allergy

Answer

Respiratory allergy

Answer

Skin Allergy

Statistics Review 2 (Topics 5 - 7)

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics