Exam 6: Normal Probability Distributions

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%.

If a histogram of a sample of men's ages is skewed, what do you expect to see in the normal quantile plot?

A normal quartile plot is given below for the lifetimes (in hours) of a sample of batteries of a particular brand. Use the plot to assess the normality of the lifetimes of these batteries. Explain your reasoning.

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5?

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

The heights of adult females are normally distributed. If you were to construct a histogram o? 40 randomly selected women, what shape would the histogram of those heights have and what Pattern would you expect in a normal quantile plot of these data?

Heights of adult females are normally distributed. Samples of height of adult females, each of size n = 3, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as a normal distribution because the sample size is so small? Explain.

Scores on a test have a mean of 70 and $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ . (You will need to first find the standard deviation.)

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

Find the area of the shaded region. The graph depicts the standard normal distribution wit? mean 0 and standard deviation 1.

The continuity correction is used to compensate for the fact that a ___________distribution is used to approximate a ____________ distribution.

Identify three important criteria to determine if the use of a normal distribution is justified?

A normal quartile plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6 . What are the values of the mean and standard deviation after all test scores have been standardized by converting them to $z$ -scores using $z = ( x - \mu ) / \sigma$ ?

You will use a normal distribution to approximate a binomial distribution. Complete the following table for a distribution in which $\mu = 16$ . It might be helpful to make a diagram to help you determine the continuity factor for each entry. Find the probability that The continuity correction factor is: x is at least 12 x is at most 12 x is more than 12 x is less than 12

If $z$ is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27$ )

Scores on a test are normally distributed with a mean of $63.2$ and a standard deviation of $11.7$ . Find $P _ { 81 }$ , which separates the bottom $81 \%$ from the top $19 \%$ .

If a sample size is <_____ , the sample size must come from a population having a normal distribution in order to follow normal distribution calculations.