# Test Bank: Introduction to Probability and Statistics

**Topics:**Normal distribution, Standard deviation, Probability theory

**Pages:**21 (3883 words)

**Published:**December 2, 2012

1.The standard deviation of any normal random variable is always equal to one.

Answer: False Type: Concept Difficulty: Easy

2.For any normal random variable, the probability that the random variable will equal one is always zero.

Answer: True Type: Concept Difficulty: Medium

3.The graph of a standard normal random variable is always symmetric.

Answer: True Type: Concept Difficulty: Easy

4.The formula will convert any normal distribution into the “standard normal distribution.”

Answer: True Type: Concept Difficulty: Easy

5.Any normal random variable with standard deviation equal to one is a standard normal random variable.

Answer: False Type: Concept Difficulty: Medium

6.The notation X - N(4, 32) indicates a normal distribution with mean 2 and standard deviation 3.

Answer: False Type: Concept Difficulty: Easy

7.The total area under a normal curve is always equal to one.

Answer: True Type: Concept Difficulty: Easy

8.The notation Z - N(0, 1) indicates a standard normal distribution.

Answer: True Type: Concept Difficulty: Easy

9.The probability that a normal random variable will be within two standard deviations of its mean is approximately 0.68.

Answer: False Type: Concept Difficulty: Easy

10.The normal distribution is a continuous distribution.

Answer: True Type: Concept Difficulty: Easy

11.The normal distribution can be used to approximate the binomial distribution when both np and n(1 - p) are at least five.

Answer: True Type: Concept Difficulty: Easy

12.The normal distribution approximation to the binomial works best when n is large.

Answer: True Type: Concept Difficulty: Easy

13.The formula can be used with both a normal and binominal distribution.

Answer: True Type: Concept Difficulty: Easy

Multiple Choice Questions

14.Find P(-2 < Z < 2).

A)0.9544

B)0.4772

C)0.9772

D)0.6826

E)none of the above

Answer: A Type: Computation Difficulty: Easy

15.Find P(-0.5 < Z < 0.5).

A)0.3830

B)0.1915

C)0.6515

D)0.3085

E)none of the above

Answer: A Type: Computation Difficulty: Easy

16.What is the probability that a standard normal variable will be between -0.5 and 1.00? A)0.2857

B)0.5328

C)0.6687

D)0.2500

E)none of the above

Answer: B Type: Computation Difficulty: Easy

17.Find the probability that a standard normal random variable has a value greater than -1.56. A)0.0332

B)0.0594

C)0.9406

D)0.9668

E)none of the above

Answer: C Type: Computation Difficulty: Easy

18.Let X be a normally distributed random variable with mean 100 and standard deviation 20. Find two values, a and b, symmetric about the mean, such that the probability of the random variable being between them is 0.99. A)90.5, 105.9

B)80.2, 119.8

C)22, 78

D)48.5, 151.5

E)90.1, 109.9

Answer: D Type: Computation Difficulty: Medium

19.A professor grades his students on a normal distribution, with mean at 75 and standard deviation of 15. If there are 39 students in his class, about how many score between 80 and 90? A)5

B)21

C)8

D)13

E)none of the above

Answer: C Type: Computation Difficulty: Hard

20.A calculator manufacturer performs a test on its calculators and finds their working life to be normally distributed, with a mean of 2,150 hours and a standard deviation of 450 hours. What should the manufacturer advertise as the life of the calculators so that 90% of the calculators are covered? A)2,555

B)1,947

C)1,410

D)1,745

E)1,574

Answer: E Type: Computation Difficulty: Hard

21.You have two stocks: A and B. The price of each stock...

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