Exam 6: The Normal Probability Distribution

Water Usage Narrative The mayor of the city of Windsor was informed that household water usage is a normally distributed random variable with a mean of 95 litres and a standard deviation of 16 litres per day. -Refer to Water Usage Narrative. Find the probability that a randomly chosen household uses less than 79 litres per day.

If z is a standard normal random variable, how does the area between z = 0.0 and z = 1.25 compare to the area between z = 1.25 and z = 2.5?

Given that Z is a standard normal variable, and P(Z b) = 0.2580, which of these values is b?

For some positive value of x, the probability that a standard normal variable is between 0 and +1.5x is 0.4332. What is the value of x?

University Faculty Survey Narrative A recent survey of university faculty reported 55% were considering going into another profession. -Refer to University Faculty Survey Narrative. Based on this information, what is the expected number of faculty who would be considering going into another profession if we randomly sampled 200 faculty members?

Textbook Narrative Twenty-five psychology instructors have formed a committee to pick next year's textbook, and they have narrowed their decision down to two equally good books, one with a better bibliography and references, and the other with a better format and illustrations. Since the books are considered to be equally good, we will assume the probability an instructor chooses either book is 0.5 and the instructors' decisions are made independently. -Refer to Textbook Narrative. Use the normal approximation to the binomial to find the probability 15 or more instructors choose the book with the better format and illustrations.

Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. a. Find the 90th percentile. b. Find the 95th percentile. c. Find the 5th percentile.

If Z is a standard normal random variable, how would one describe the area between z = 0.0 and z =1.50 compared to the area between z = 1.5 and z = 3.0?

Which of the following must be specified in order to completely determine the probability density function f(x) of a random variable X that is normally distributed?

The normal approximation to the binomial distribution works best when the number of trials is large, and when the binomial distribution is symmetrical (like the normal distribution).

Given that Z is a standard normal random variable, a negative value of Z indicates that the standard deviation of Z is negative.

If Z is a standard normal random variable, then which of these values is the value of z for which P(-z Z z) equals 0.8764?

College Applicants Narrative The admissions office of a community college in Ontario is asked to accept deposits from a number of qualified prospective freshmen so that, with probability of about 0.95, the size of the freshmen class will be less than or equal to 150. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the freshmen class if accepted. -Refer to College Applicants Narrative. If applicants in the number determined in the previous question are accepted, what is the probability that the freshmen class size will be less than 135?

The possible observations of continuous random variables are infinite in number. Characteristics measured in units of money, time, distance, height, volume, length, or weight are examples of such variables.

Given that Z is a standard normal random variable, which of these is the value of z if the area to the right of z is 0.1949?

The proportion of the total area under the normal curve that lies within one standard deviation of the mean is approximately 0.75.

In general, the binomial probability P(X x) is approximated by the area under the normal curve to the left of x + -0.5.

Using the standard normal curve, the area between z = 0 and z = 2.2 is 0.4868.

University Football Narrative A student government representative claims that 55% of the student body of a local university favour a move to Division I in university football. A random sample of 2000 students is selected. -Refer to University Football Narrative. What is the approximate probability that fewer than 1150 students of the 2000 selected will favour the move to Division I?

Which of the following correctly describes the normal probability distribution?