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Chapter Questions
Scores on a quiz were normally distributed and had a mean of 10 and a standard deviation of $3 .$ For each ofthe following scores, find the $Z$ score and the percentage of area above and below the score.
Assume that the distribution of a college entrance exam is normal, with a mean of 500 and a standard deviation of 100 . For each of the following scores, find the equivalent $Z$ score, the percentage of the area above the score, and the percentage of the area below the score.
The senior class has been given a comprehensive examination to assess educational experience. The mean on the test was 74 and the standard deviation was 10 . What percentage of the students had scoresa. between 75 and 85 ?b. between 80 and 85 ?c. above $80 ?$d. above 83 ?e. between 80 and $70 ?$f. between 75 and $70 ?$g. below 75 ?h. below 77 ?i. below 80 ?j. below 85 ?
For a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area isa. between the scores of 40 and 47 ?b. above a score of 47 ?c. below a score of 53 ?d. between the scores of 35 and $65 ?$e. above a score of 72 ?f. below a score of 31 and above a score of $69 ?$g. between the scores of 55 and 62 ?h. between the scores of 32 and $47 ?$
At St. Algebra College, the 200 freshmen enrolled in introductory biology took a final exam on which their mean score was 72 and their standard deviation was 6 . The following table presents the grades of 10 students. Convert each into a Z score and determine the number of people who scored higher or lower than each of the 10 students. (HINT: Multiply the appropriate proportion by $N$ and round the result.)
If a distribution of test scores is normal, with a mean of 78 and a standard deviation of 11 , what percentage of the area liesa. below 60 ?b. below $70 ?$c. below 80 ?d. below 90 ?e. between 60 and $65 ?$f. between 65 and 79 ?g. between 70 and 95 ?h. between 80 and 90 ?i. above $99 ?$i. above 89 ?k. above 75 ?l. above 65 ?
A scale measuring prejudice has been administered to a large sample of respondents. The distribution of scores is approximately normal, with a mean of 31 and a standard deviation of $5 .$ What percentage of the sample had scoresa. below 20 ?b. below 40 ?c. between 30 and 40 ?d. between 35 and $45 ?$e. above 25 ?f. above 35 ?
On the scale mentioned in problem $5.7$, if a score of 40 or more is considered "highly prejudiced," what is the probability that a person selected at random will have a score in that range?
For a math test on which the mean was 59 and the standard deviation was 4, what is the probability that a student randomly selected from this class will have a scorea. between 55 and 65 ?b. between 60 and 65 ?c. above $65 ?$d. between 60 and $50 ?$e. between 55 and 50 ?f. below 55 ?
The average number of drop-outs for a school district has been 305 per year with a standard deviation of50. What is the probability that next year the number of drop-outs will bea. less than $250 ?$b. less than 300 ?c. more than 350 ?d. more than 400 ?e. between 250 and $350 ?$f. between 300 and $350 ?$g. between 350 and 375 ?
The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top $15 \%$ on this test. If the mean score this year is 87 and the standard deviation is 8 , would an individual with a score of 110 be accepted?
To be accepted into an honor society, students must have GPAs in the top $10 \%$ of the school. If the mean GPA is $2.78$ and the standard deviation is $.33$, which of the following GPAs would qualify?$$3.20,3.21,3.25,3.30,3.35$$
In a distribution of scores with a mean of 35 and a standard deviation of 4, which event is more likely: that a randomly selected score will be between 29 and 31 or that a randomly selected score will be between 40 and 42 ?
After taking the state merit examinations for the positions of school counselor and social worker, you receive the following information on the tests and on your performance. On which of the tests did you do better?$$\begin{aligned}&\begin{array}{ll}\hline \text { School Counselor } & \text { Social Worker } \\\hline \bar{X}=118 & \bar{X}=27 \\s=17 & s=3 \\\text { Your score }=127 & \text { Your score }=29\end{array}\\&\begin{aligned}&\end{aligned}\end{aligned}$$