Q16 Standard Normal Distribution. Fi... [FREE SOLUTION] (2025)

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Short Answer Step by step solution Given information Describe the z-score State the relationship between the area and the probability Find the z-score One App. One Place for Learning. Most popular questions from this chapter Recommended explanations on Math Textbooks Statistics Calculus Probability and Statistics Geometry Decision Maths Theoretical and Mathematical Physics Study anywhere. Anytime. Across all devices.

Chapter 6: Q16 (page 241)

Standard Normal Distribution. Find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Short Answer

Expert verified

The z-score indicated in graph is 0.82.

Step by step solution

Given information

The bone density score follows the standard normal distribution with a mean of 0 and a standard deviation of 1.

Describe the z-score

The z-score is the distance along the horizontal scale of the standard normal distribution (corresponding to the number of standard deviations above or below the mean). These are the values taken by the standard normal distribution, represented by Z.

State the relationship between the area and the probability

As the standard normal curve has an area of 1 enclosed under the curve, the area has a one-to-one correspondence with the probability.

The left-tailed area is equal to the cumulative probabilities, which are obtained by using the standard normal table (Table A-2) for z-scores.

To find the required right-tailed area, subtract the cumulative probabilities from 1.

Find the z-score

The area represented is mathematically represented as

$Area to the right of z = P (Z > z) 0.2061 = 1 - P (Z < z) P (Z < z) = 1 - 0.2061 P (Z < z) = 0.7939$

The z-score that has the area of 0.7939 to the left of it is obtained from the standard normal table as follows.

From the standard normal table, the area of 0.7939 is observed corresponding to the row value of 0.8 and the column value of 0.02, which implies that the z-score is 0.82.

Thus, the indicated z-score value with the right-tailed area of 0.2061 is 0.82.

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Most popular questions from this chapter

Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answersto four decimal places.Greater than -2.00.Using a Formula to Describe a Sampling Distribution Exercise 15 “Births” requires the construction of a table that describes the sampling distribution of the proportions of girls from two births. Consider the formula shown here, and evaluate that formula using sample proportions (represented by x) of 0, 0.5, and 1. Based on the results, does the formula describe the sampling distribution? Why or why not?Px=122-2x!2x!wherex=0,0.5,1Continuous Uniform Distribution. In Exercises 5–8, 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.Less than 4.00 minutesStandard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answersto four decimal places.Greater than -3.05.In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.Sampling Distribution of the Sample Mediana. Find the value of the population median.b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-3. (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not?

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