313 Use Table A to find the value z of a standard Normal var

(3.13) Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis.

(a) The point z with 61% of the observations falling below it

z (±0.01) =

(b) The point z with 20% of the observations falling above it

z (±0.01) =

(3.18 AQ) The figure below shows a Normal curve.

The standard deviation of this distribution is

(S-AQ 3.59) There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209.

Reports on a student\'s ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one.

Tanya scores 1294 on the SAT. What is her percentile (± 1)?    %

(S-AQ 3.60) There are two major tests of readiness for college: the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209.

The SAT scores that make up the top 25% of all scores range from    to 1600.
(Round your answer to the nearest whole number.)

(S-AQ 3.61) Suppose the scores on the ACT test for last year\'s high school graduating class had mean 20.9 and standard deviation 4.8. In all, 1,165,363 students in this class took the test, and 1,048,464 of them had scores of 28 or lower.

If the distribution of scores were Normal, what percent (± 0.1) of scores would be 28 or lower?    %

What percent (± 0.1) of the actual scores were 28 or lower?    %

(S-AQ 3.63) The distribution of heights of women aged 20 to 29 is approximately Normal with mean 65.3 inches and standard deviation 3.3 inches.

The height (± 0.1 inch) of the middle 95% of young women falls between a low of    inches and a high of   inches.

(Example 3.7 AQ) The National Collegiate Athletic Association (NCAA) uses a sliding scale for eligibility for Division I athletes. Those students with a 2.5 high school GPA must score at least 820 on the combined mathematics and critical reading parts of the SAT to compete in their first college year. The combined scores of the almost 1.7 million high school seniors taking the SAT in 2013 were approximately Normal with mean 1011 and standard deviation 216.

What percent of seniors score at least 820 (+/-0.1)? Use Table A to find your answer.

%

Solution

9.

(a)

Z~N(0,1)

P(Z<z)=0.61

then z= 0.279319

So, the required answer is 0.28

(b)

P(Z>z)=0.20

then, P(Z<=z)=1-0.20=0.80

so, z=0.8416212

Thus, the required answer is 0.84