# STAT200 Week 6 Quiz

May 16, 2017

**STAT200 Week 6 Quiz in $50 Only**

1. A probability is a number p such that:

A. 0 < p < 1

B. 0 ≤ p ≤ 1

C. -1 < p < 1

D. -1 ≤ p ≤ 1

E. None of the above

02. The Complement rule states that the probability of an event not occurring is

A. equal to one minus the probability it will occur.

B. equal to one minus the probability it will not occur.

C. equal to 0.0

D. equal to 1.0

E. None of the above**03. A tire manufacturer claims that the probability of its XLT tire lasting 50,000 miles or more is 0.80. If three XLT tires are installed on a car what is the probability that all three will last 50,000 miles or more?**

A. 0.800.

B. 0.640.

C. 0.240.

D. 0.512.

E. None of the above

04. In how many different ways can a work party of 4 be chosen from 9 volunteers?

A. 4

B. 36

C. 126

D. 3024

E. None of the above

05. Which of the following is/are properties of the Binomial Distribution?

A. The number of trials is fixed in advance.

B. The trials are independent.

C. Each trial has exactly two outcomes.

D. The probability of success is the same for each trial.

E. All of the above.

06. A fair coin is tossed 6 times. What is the probability of getting exactly 3 heads in the 6 tosses?

A. 0.2

B. 0.3

C. 0.4

D. 0.5

E. None of the above

07. The mean of a probability distribution is referred to as the

A. median

B. mode

C. expected value

D. weighted mean

E. none of the above

08. The number of armed robberies and their probabilities, in a particular city in a month, are given in the table below:

Number of armed robberies

Probability

1

0.05

2

0.30

3

0.40

4

0.25

How many armed robberies on the average should be expected on a typical month?

A. 10.00

B. 2.50

C. 2.85

D. 3.01

E. None of the above

09. A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both. The probability that a cell phone sold last month had a camera or a music player is

A. 0.92

B. 0.70

C. 0.18

D. 0.36

E. None of the above

10. The probability of two events occurring together is referred to as

A. a marginal probability

B. a conditional probability

C. a subjective probability

D. the multiplication rule

E. a joint probability

11. A student’s score on a test is 110. The scores are normally distributed with mean µ = 120 and standard deviation σ = 8. Find the student’s z-score.

A. 1.25

B. -1.25

C. -1.52

D. 0.25

E. None of the above

12. To construct a normal distribution, the measurements needed are

A. the mean and the median

B. the mode and the standard deviation

C. the median and the standard deviation

D. the standard deviation and the variance

E. none of the above

13. Which of the following is not a property of the standard normal distribution?

A. It is continuous

B. It is uniform

C. It is bell-shaped

D. It is unimodal

E. The curve never touches the horizontal axis.

14. Consider the Standard Normal distribution. Find P(-0.73 < z < 2.21)

A. -0.7537

B. 0.9987

C. 0.7534

D. 0.7537

E. none of the above

15. Consider the Standard Normal distribution. Find the probability P(z > 0.59)

A 0.7224

B 0.2190

C 0.2224

D 0.2776

E None of the above

16. Consider the Standard Normal distribution. Find the probability that z is less than -1.82.

A. 0.0351

B. -0.0344

C. 0.0344

C.0.9656

E. none of the above

17. Find the value of z such that the area to the left of z is 9% of the total area under the curve.

A. 0.82

B. -0.82

C. 1.34

D. -1.34

E. none of the above

18. Find the value of z such that the area to the right of z is 67% of the total area under the standard normal curve.

A 0.44

B -0.44

C 1.00

D -1.50

E None of the above

19. Find the value of z such that the area between –z and +z is 98% of the total area under the standard normal curve.

A. 2.02

B. 1.96

C.

Correct answer 2.33 (to be precise 2.326)

20. The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming a normal distribution, what is the probability that a family spends more than $410 per month?

A. 0.1151

B. 0.1539

C. 0.8849

D. 0.8461

E. none of the above

21. If a population is normally distributed, the distribution of the sample means for a given sample size n will

A. be positively skewed.

B. be negatively skewed.

C. be uniform.

D. be normal.

E. none of the above

22. If a population is not normally distributed, the distribution of the sample means for a given sample size n will

A. take the same shape as the population.

B. approach a normal distribution as n increases.

C. be positively skewed.

D. be negatively skewed.

E. none of the above

23. An auditor takes a random sample of size n=110 from a large population. The population standard deviation is not known, but the sample standard deviation is s = 48. Find the standard error of the mean.

A. 48

B. 4.58

C. 0.44

D. 2.29

E. None of the above

24. The scores on a certain test are normally distributed with mean 61 and standard deviation 3. What is the probability that a sample of 100 students will have a mean score more than 61.3?

A. 0.4602

B. 0.3413

C. 0.8413

D. 0.1587

E. none of the above

25. A random sample of 66 observations was taken from a large population. The population proportion is 12%. The probability that the sample proportion will be more than 17% is

A. 0.0568

B. 0.8944

C. 0.1056

D. 0.4222

E. none of the above

26. When the 99% confidence interval is calculated instead of the 95% confidence interval with the sample size n being the same the margin of error will be

A. smaller.

B. larger.

C. the same.

D. reduced by 4%

E. none of the above

27. As the sample size increases,

A. the population standard deviation decreases

B. the population standard deviation increases

C. the standard error increases.

D. the standard error decreases.

E. none of the above

28. Statistical inference

A. is reasoning from a sample to a population.

B. is reasoning from a population to a sample.

C. requires a large sample.

D. requires examination of the entire population.

E. is based on deductive reasoning.

29. The best point estimate of the population mean is

A. the sample mean

B. the sample median

C. the sample mode

D. the sample midrange

E. none of the above.

30. A 95% confidence interval based on a sample for the mean time it takes to process a claim by an insurance company is between 10 and 15 days. This means that

A. only 5% of all claims take less than 10 or more than 15 days to process.

B. only 5% of all claims take between 10 and 15 days to process.

C. about 95% of all intervals similarly constructed from samples of the same size will contain the true population mean processing time.

D. the probability is 0.95 that all claims take between 10 and 15 days o process.

E. none of the above

31. A sample of 31 people was randomly selected from among the workers in a large shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 2.2 minutes. From another study we know that the population standard deviation was 0.72 min. The 90% confidence interval for the true population mean time µ to polish a shoe is

A. (1.98, 2.42)

B. (1.95, 2.45)

C. (1.90, 2.50)

D. (1.99, 2.41)

E. none of the above

32. From a large approximately normal population 30 people are selected at random. If the sample mean age is 85.1 years and the sample standard deviation is 4.5 years, the 95% confidence interval for the true population mean is

A. (83.49, 86.71)

B. (83.46, 86.74)

C. (83.42, 86.78)

D. (83.39, 86.81)

E. none of the above

33. Find t*, the critical t value for a confidence level of 99% and a sample size of 17.

A. 2.898

B. 2.583

C. 2.921

D. 2.567

E. none of the above

34. The Labor Department wants to estimate the percentage of females in the U.S. labor force. They select a random sample of 525 employment records, and find that 210 of the people are females. The 90% confidence interval is

A. (0.3648, 0.4352)

B. (0.3581, 0.4419)

C. (0.3449, 0.4551)

D. (0.4235, 0.5679)

E. None of the above

35. If the Department of Labor wishes to tighten its interval, they should

A. Increase the confidence level.

B. Increase the sample size.

C. Decrease the sample size.

D. Both A and B

E. Both A and C

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