In a normal distribution, how are the mean and the median related? Why?A job-applicant test consisted of three parts: verbal, quantitative, and logical reasoning. The mean and standard deviation for each part are given below. VERBALQUANTITATIVELOGICAL REASONINGMean8411814Standard Deviation10184 a. Applicant A scores were 90 on verbal, 133 on quantitative, and 18 on logical reasoning. Determine the applicant’s z-score for each part.b. Use the answers in (a) to determine each of the following:i. On which part did the applicant perform relatively the highest?ii. On which part did the applicant perform relatively the lowest?iii. To determine an overall composite score, we find the mean of the z-scores. What is the applicant’s composite score?3. A professor gave final examination to 110 students. Eighteen students had scores that were more than 1 standard deviation above the mean. With this information, can you conclude that 18 of the students had scores that were more than 1 standard deviation below the mean? Explain.4. A psychologist finds that the intelligence quotients (IQ) of a group of patients are normally distributed, with a mean of 102 and a standard deviation of 16. Find the percent of the patients with IQs a. above 114 b. between 90 and 118.5. The resting heart rates of a group of healthy adult men were found to have a mean of 73.4 beats per minute, with a standard deviation of 5.9 beats per minute. What percent of the men had a resting heart rate ofa. greater than 80 beats per minute?b. between 70 and 85 beats per minute? a T s enoute sean ere, we find the mean of the scores. What is thehemumAQA. aax- - AC eB/U-A-XX A AA E aa0.TASK 1: NORMAL DISTRIBUTION1 na normal distribution, how are the mean and the median related? Why?2 Ajob-applicant test consisted of three parts verbal, quantitative, and logical reasoning. Themean and standard deviation for each part are given below.Poing tey|QUANTITATIVE LOGKAL REASONING118VERBAL8410MeanStandard Deviationa. Applicant A sceres were 90 en vertal, 13 on quantitative, and 18 on logcal reanoning14Heading 1Heading 2Determine the applicant's score for each part.b. Use the antwers in (a) to determine each of the followingL On which part did the appicant pertorm relatively the highest?L On which part did the applicant perform relatively the lowest?Heading 3Heading4oing3. Aprofessor gave final examination to t110 students. Eighteen students had scores that weremore than 1 standard deviation above the mean. With this information, can you conclude that18 of the students had scores that were more than i standard deviation below the mean?Explain.4. A poychologist finds that the intelligence quotients (Q) ofa group of patients are normallydistributed, with a mean of 102 and a tandard deviation of 16. Find the percent of the patientswith Os above 1145. The resting heart rates of a group of healthy adut men were found to have a mean of 714 beatsper minute, with a standard deviation of s9 beats per minute. What percent of the men hadaresting heart rate ofa. greater than B0 beats per minutetb. between 90 and 118.between 70 and 85 beats per minune?

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In a normal distribution, how are the mean and the median related? Why?
A job-applicant test consisted of three parts: verbal, quantitative, and logical reasoning. The mean and standard deviation for each part are given below.

	VERBAL	QUANTITATIVE	LOGICAL REASONING
Mean	84	118	14
Standard Deviation	10	18	4

a. Applicant A scores were 90 on verbal, 133 on quantitative, and 18 on logical reasoning.

Determine the applicant’s z-score for each part.

b. Use the answers in (a) to determine each of the following:

i. On which part did the applicant perform relatively the highest?

ii. On which part did the applicant perform relatively the lowest?

iii. To determine an overall composite score, we find the mean of the z-scores. What is the

applicant’s composite score?

3. A professor gave final examination to 110 students. Eighteen students had scores that were more than 1 standard deviation above the mean. With this information, can you conclude that 18 of the students had scores that were more than 1 standard deviation below the mean? Explain.

4. A psychologist finds that the intelligence quotients (IQ) of a group of patients are normally distributed, with a mean of 102 and a standard deviation of 16. Find the percent of the patients with IQs

a. above 114 b. between 90 and 118.

5. The resting heart rates of a group of healthy adult men were found to have a mean of 73.4 beats per minute, with a standard deviation of 5.9 beats per minute. What percent of the men had a resting heart rate of

a. greater than 80 beats per minute?

b. between 70 and 85 beats per minute?

a T s enoute sean ere, we find the mean of the scores. What is the
hemum
AQA. aax- - AC e
B/U-A-XX A AA E aa0.
TASK 1: NORMAL DISTRIBUTION
1 na normal distribution, how are the mean and the median related? Why?
2 Ajob-applicant test consisted of three parts verbal, quantitative, and logical reasoning. The
mean and standard deviation for each part are given below.
Poing tey
|QUANTITATIVE LOGKAL REASONING
118
VERBAL
84
10
Mean
Standard Deviation
a. Applicant A sceres were 90 en vertal, 13 on quantitative, and 18 on logcal reanoning
14
Heading 1
Heading 2
Determine the applicant's score for each part.
b. Use the antwers in (a) to determine each of the following
L On which part did the appicant pertorm relatively the highest?
L On which part did the applicant perform relatively the lowest?
Heading 3
Heading4
oing
3. Aprofessor gave final examination to t110 students. Eighteen students had scores that were
more than 1 standard deviation above the mean. With this information, can you conclude that
18 of the students had scores that were more than i standard deviation below the mean?
Explain.
4. A poychologist finds that the intelligence quotients (Q) ofa group of patients are normally
distributed, with a mean of 102 and a tandard deviation of 16. Find the percent of the patients
with Os above 114
5. The resting heart rates of a group of healthy adut men were found to have a mean of 714 beats
per minute, with a standard deviation of s9 beats per minute. What percent of the men hada
resting heart rate of
a. greater than B0 beats per minutet
b. between 90 and 118.
between 70 and 85 beats per minune?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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