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Chapter 2: Q. 2.3 (page 119)

Use Table A in the back of the book to find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.

3.鈭�0.56<z<1.81

Short Answer

Expert verified

The standard Normal curve, with the region represented by the area, is as follows:

Step by step solution

01

Given Information   

Z-score :鈭�0.56<z<1.81

02

Explanation   

From table A,

p(鈭�0.56<z<1.81)=p(z<1.81)鈭�p(<鈭�0.56)=p(z<1.81)鈭�[1鈭�p(z<0.56)]=0.9649鈭�[1鈭�0.7123]=0.9648鈭�0.2877=0.6771

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Most popular questions from this chapter

Measuring bone density Individuals with low bone density have a high risk of broken bones (fractures). Physicians who are concerned about low bone density (osteoporosis) in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). A patient who undergoes a DEXA test usually gets bone density results in grams per square centimeter(g/cm2)and in standardized units. Judy, who is 25years old, has her bone density measured using DEXA. Her results indicate a bone density in the hip948g/cm2and a standardized score ofz=鈭�1.45. In the reference population of For 25-year-old women like Judy, the mean bone density in the hip is 956g/cm2

(a) Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score tells her about her bone density.

(b) Use the information provided to calculate the standard deviation of bone density in the reference population.

Each year, about 1.5million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was 46.9and the standard deviation was10.9. Nationally, 5.2%of test takers earned a score of 65 or higher on the Critical Reading test鈥檚 20to 80scale.9

PSAT scores Scott was one of 50junior boys to take the PSAT at his school. He scored 64on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all 50boys鈥� Critical Reading scores, the mean was 58.2and the standard deviation was 9.4

(a) Write a sentence or two comparing Scott鈥檚 percentile among the national group of test-takers and among the 50boys at his school.

(b) Calculate and compare Scott鈥檚 z-score among these same two groups of test-takers.

Which of the following is least likely to have a nearly Normal distribution?

(a) Heights of all female students taking STAT 001 at State Tech.

(b) IQ scores of all students taking STAT 001 at State Tech.

(c) SAT Math scores of all students taking STAT 001 at State Tech.

(d) Family incomes of all students taking STAT 001 at State Tech.

(e) All of (a)鈥�(d) will be approximately Normal.

Estimate Q1, Q3, and the IQR of the distribution.

Brent is a member of the school鈥檚 basketball team. The mean height of the players on the team is 76 inches. Brent鈥檚 height translates to a z-score of 鈭�0.85 in the team鈥檚 height distribution. What is the standard deviation of the team members鈥� heights?
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