0.2 Practice tests (1-4) and final exams  (Page 11/36)

5.2: the uniform distribution

47 . For the continuous probability distribution described by the function $f(x)=\frac{1}{10}$ for $0\le x\le 10$ , what is the P (2< x <5)?

Use the following information to answer the next four exercises. The number of minutes that a patient waits at a medical clinic to see a doctor is represented by a uniform distribution between zero and 30 minutes, inclusive.

48 . If X equals the number of minutes a person waits, what is the distribution of X ?

49 . Write the probability density function for this distribution.

50 . What is the mean and standard deviation for waiting time?

51 . What is the probability that a patient waits less than ten minutes?

5.3: the exponential distribution

52 . The distribution of the variable X , representing the average time to failure for an automobile battery, can be written as: X ~ Exp ( m ). Describe this distribution in words.

53 . If the value of m for an exponential distribution is ten, what are the mean and standard deviation for the distribution?

54 . Write the probability density function for a variable distributed as: X ~ Exp (0.2).

6.1: the standard normal distribution

55 . Translate this statement about the distribution of a random variable X into words: X ~ (100, 15).

56 . If the variable X has the standard normal distribution, express this symbolically.

Use the following information for the next six exercises. According to the World Health Organization, distribution of height in centimeters for girls aged five years and no months has the distribution: X ~ N (109, 4.5).

57 . What is the z -score for a height of 112 inches?

58 . What is the z -score for a height of 100 centimeters?

59 . Find the z -score for a height of 105 centimeters and explain what that means In the context of the population.

60 . What height corresponds to a z -score of 1.5 in this population?

61 . Using the empirical rule, we expect about 68 percent of the values in a normal distribution to lie within one standard deviation above or below the mean. What does this mean, in terms of a specific range of values, for this distribution?

62 . Using the empirical rule, about what percent of heights in this distribution do you expect to be between 95.5 cm and 122.5 cm?

6.2: using the normal distribution

Use the following information to answer the next four exercises. The distributor of lotto tickets claims that 20 percent of the tickets are winners. You draw a sample of 500 tickets to test this proposition.

63 . Can you use the normal approximation to the binomial for your calculations? Why or why not.

64 . What are the expected mean and standard deviation for your sample, assuming the distributor’s claim is true?

65 . What is the probability that your sample will have a mean greater than 100?

66 . If the z -score for your sample result is –2.00, explain what this means, using the empirical rule.

7.1: the central limit theorem for sample means (averages)

67 . What does the central limit theorem state with regard to the distribution of sample means?

68 . The distribution of results from flipping a fair coin is uniform: heads and tails are equally likely on any flip, and over a large number of trials, you expect about the same number of heads and tails. Yet if you conduct a study by flipping 30 coins and recording the number of heads, and repeat this 100 times, the distribution of the mean number of heads will be approximately normal. How is this possible?