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Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -2 and z = 2 (or within 2 standard deviation of the mean).

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -3 and z = 3 (or within 3 standard deviation of the mean).

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard deviation of the mean).

Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are

a. significantly high (or at least 2 standard deviations above the mean).

b. significantly low (or at least 2 standard deviations below the mean).

c. not significant (or less than 2 standard deviations away from the mean).

Probability if 0 For Formula 5-9, what does P(0) represent? Simplify Formula 5-9 for the case in which x = 0.

Bone Density Test. In Exercises 1鈥�4, assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1.

Bone Density For a randomly selected subject, find the probability of a score between 0.87 and 1.78.

Blue Eyes Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University).

a. Let B denote the event of selecting someone who has blue eyes. What does the event \(\overline {\bf{B}} \) denote?

b. Find the value of P(\(\overline {\bf{B}} \)).

c. Find the probability of randomly selecting three different people and finding that all of them have blue eyes.

d. Find the probability that among 100 randomly selected people, at least 40 have blue eyes.

e. If 35% of us really do have blue eyes, is a result of 40 people with blue eyes among 100 randomly selected people a result that is significantly high?

Sampling Distributions Scores on the Gilliam Autism Rating Scale (GARS) are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 64 GARS scores is randomly selected and the sample mean is computed.

a. Describe the distribution of such sample means.

b. What is the mean of all such sample means?

c. What is the standard deviation of all such sample means?

Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.

Greater than 3.00 minutes

Unbiased Estimators

a. What is an unbiased estimator?

b. For the following statistics, identify those that are unbiased estimators: mean, median, range, variance, proportion.

c. Determine whether the following statement is true or false: 鈥淭he sample standard deviation is a biased estimator, but the bias is relatively small in large samples, so is often used to estimate $蟽$鈥�