Exam 6: The Normal Probability Distribution

Which of the following distributions are always symmetrical?

Which of the following is NOT a characteristic of the normal distribution?

If x is a normal random variable with mean of 2 and standard deviation of 5, then P(x < 3) = P(x > 7).

Given that z is a standard normal random variable, a value of z that is equal to 0 indicates that the standard deviation of z is also 0.

Which of the following statements best describes a standard normal distribution?

For a continuous random variable x, the probabilities P(0 < x < 1) and P(0 < x < 1) are always equal.

Let be a z-score that is unknown but identifiable by position and area. If the area to the right of is 0.7088, then what is the value of ?

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

In the standard normal curve, the z-score representing the 10th percentile is 1.28.

Pacific Salmon Narrative The owner of a fish market determined that the average weight for a Pacific salmon is 3.6 kg, with a standard deviation of 0.8 kg. Assume the weights of the salmon are normally distributed. -Refer to Pacific Salmon Narrative. A randomly selected salmon will weigh more than x kg to be one of the top 5% in weight. What is the value of x?

Learning Time of Computer Software Narrative The time x a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. -Refer to Learning Time of Computer Software Narrative. What is the probability that the student spends less than 6 hours learning the software package?

Suppose the current median age of Canadian citizens is 30. If a survey of 500 randomly selected Canadian citizens is conducted, what is the probability that, at most, 240 of them will be under 30 years old?

Continuous random variables that can assume values at all points on an interval of values, with no breaks between possible values, are quite common. Which of the following items could NOT be classified as a continuous random variable?

For a continuous random variable x and constant a, P(x a) = P(x > a) because P(x = a) = 0.

Given a normal random variable x with mean and standard deviation , the standard normal random variable associated with x is .

Two students are enrolled in an introductory statistics class at the university. The first student is in a morning section and the second student is in an afternoon section. If the student in the morning section takes a midterm exam and earns a score of 76, and the student in the afternoon section takes a midterm exam and earns a score of 72, which student performed better compared to the rest of the students in his or her respective class? Assume test scores are normally distributed. In the morning section, the mean was 64 and the standard deviation was 8. In the afternoon section, the class mean was 60 with a standard deviation of 7.5

For any random variable x, P(x = a) = 0.

Given that X is a binomial random variable, the binomial probability P(X x) is approximated by the area under a normal curve to the left of which of the following values?

One difference between a binomial random variable x and a standard normal random variable z is that with the binomial random variable we cannot determine P(x = a), while for the standard normal variable we can determine P(z = a).

Pacific Salmon Narrative The owner of a fish market determined that the average weight for a Pacific salmon is 3.6 kg, with a standard deviation of 0.8 kg. Assume the weights of the salmon are normally distributed. -Refer to Pacific Salmon Narrative. Below what weight do 83.4% of the weights occur?