Exam 6: The Normal Probability Distribution

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

The owner of a fish market determined that the average weight for a catfish is 3.6 pounds with a standard deviation of 0.8 pound. Assume the weights of catfish are normally distributed. What is the probability that a randomly selected catfish will weigh more than 4.8 pounds? ______________ What is the probability that a randomly selected catfish will weigh between 3 and 5 pounds? ______________ A randomly selected catfish will weigh more than x pounds to be one of the top 5% in weight. What is the value of x? ______________ A randomly selected catfish will weigh less than x pounds to be one of the bottom 20% in weight. What is the value of x? ______________ Above what weight (in pounds) do 87.70% of the weights occur? ______________ What is the probability that a randomly selected catfish will weigh less than 3.2 pounds? ______________ Below what weight (in pounds) do 83.4% of the weights occur? ______________

The average length of time required to complete a college achievement test was found to equal 75 minutes, with a standard deviation of 15 minutes. When should the test be terminated if you wish to allow sufficient time for 90% of the students to complete the test? (Assume that the time required to complete the test is normally distributed.) ______________

Given that Z is a standard normal random variable, P(Z > -1.58) is:

If x is normally distributed random variable with a mean of 8.20 and variance of 4.41, and that P(x > b) = .08, then the value of b is:

Given a normal random variable x with mean and standard deviation , the mean of the standard normal random variable z associated with x is 1.

For some positive value of z, the probability that a standard normal variable is between 0 and z is 0.3770. The value of z is:

Assume that x is normally distributed random variable with a mean of and a standard deviation of .15. Given this information and that P(x < 2.10) = .025, what is the value of ?

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:

The probability density function f(x) of a random variable X that is normally distributed is completely determined once the:

Assume that x is a normally distributed random variable with a mean equal to 13.4 and a standard deviation equal to 3.6. Given this information and that P(x > a) = .05, the value of a must be 19.322.

The gestation time for human babies is approximately normally distributed with an average of 280 days and a standard deviation of 12. Find the upper quartile for the gestation times. ______________ Find the lower quartile for the gestation times. ______________ Would it be unusual to deliver a baby after only 6 months of gestation? ______________ Explain. ________________________________________________________

Which of the following is not true for a normal distribution?

For a car traveling 35 miles per hour (mph), the distance required to brake to a stop is normally distributed with mean of 55 feet and a standard deviation of 8 feet. Suppose you are traveling 35 mph in a residential area and a car moves abruptly into your path at a distance of 65 feet. If you apply your brakes, what is the probability that you will brake to a stop within 45 feet or less? ______________ Within 55 feet or less? ______________ If the only way to avoid a collision is to brake to a stop, what is the probability that you will avoid the collision? ______________

Let x be a binomial random variable with n = 25 and p = 0.3. Is the normal approximation appropriate for this binomial random variable? ______________ Find the mean for x. ______________ Find the standard deviation for x. ______________ Use the normal approximation to find . ______________ Use the cumulative binomial probabilities table in Appendix 1 of your book to calculate the exact probability, above. ______________ Compare the results of the last two questions. Was your approximation close, or far, from the exact answer? ______________

The scores on a national achievement test were normally distributed, with a mean of 550 and a standard deviation of 112. If you achieved a score of 690, how far, in standard deviations, did your score depart from the mean? ______________ What percentage of those who took the examination scored higher than you? ______________

Let x denote a normal random variable with mean 30 and standard deviation 5. What x-value is the 67th percentile of this distribution? ______________

A normal random variable x has mean 54 and standard deviation 15. Would it be unusual to observe the value x = 0? ______________ Explain. ________________________________________________________

A normal random variable x has mean 36.7 and standard deviation 10. Find a value of x that has area 0.01 to its right. ______________

Let be a z score that is unknown but identifiable by position and area. If the symmetrical area between a negative and a positive is 0.8132, then the value of is: