Exam 6: The Normal Probability Distribution

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 46 and 52. ______________

The z-score representing the third quartile of the standard normal distribution is:

The mean SAT verbal score of next year's entering freshmen at the local college is 600. The college also knows 69.5% of the students scored less than 625. If the scores are normally distributed, what is the standard deviation of the SAT scores? ______________

What proportion of the data from a normal distribution is within two standard deviations from the mean?

A television set manufacturer has found the length of time until the first repair is normally distributed with a mean of 4.5 years and a standard deviation of 1.5 years. If the manufacturer wants only 10.2% of the first repairs to occur within the warranty period, how long should the warranty be? ______________ years

A random variable x is normally distributed with a mean of 250 and a standard deviation of 50. Given that x = 175, its corresponding z-score is -1.50.

Suppose the records of a motel show that, on the average, 10% of their prospective guests will not claim their reservation. If the motel accepts 218 reservations and there are only 200 rooms in the motel, what is the probability that all guests who arrive to claim a room will receive one? ______________

The more peaked a normal curve will appear,

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 the value of is:

Even though the normal probability distribution deals with continuous variables, we can use it to approximate the binomial probability distribution whenever n 30 and also n(q) 30.

Which of the following statements is true with regard to continuous random variables?

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

For some positive value of x, the probability that a standard normal variable is between 0 and + 2x is 0.1255. The value of x is:

If Z is a standard normal random variable, then P(-1.25 Z -0.75) is:

If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is:

If the mean, median, and mode are all equal for a continuous random variable, then the random variable must be normally distributed.

The distribution of final exam scores in inferential statistics class is normal with standard deviation 6. Find the mean score if 93.32% of the students received scores no higher than 90. ______________

Let z denote a standard normal random variable. Find P(z > 1.48). ______________ Find P(-0.44 < z < 2.68). ______________ Determine the value of z₀ which satisfies P(z z₀) = 0.7995. ______________ Find P(z < -0.87). ______________ Find P(-1.66 < z -0.48). ______________ Find z0 such that P(-z₀ < z < z₀) = 0.901. ______________ Find z0 such that P(z < z₀) = 0.0375. ______________ Find z0 such that P(-z₀ < z < z₀) = 0.7698. ______________

Suppose that the probability p of success on any trail of a binomial distribution equals 0.90. Then for which of the following number of trials, n, would the normal distribution provide a good approximation to the binomial distribution?

Continuous random variables can assume values at all points on an interval, with no breaks between possible values.