(QUIZ)Normal distribution (Empirical and Z-scores)

The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 0.5 oz. Using the empirical rule, what percentage of the oranges from the orchard weigh between 5.5 oz. and 7.5 oz.?

• 68%
• 34%
• 95%

• 99.7%

Find the z-score for 75 given a mean of 60 and a standard deviation of 6.

• -2.5

• 2.5

• -1.15

• 1.15

Tags

CCSS.HSS.ID.A.4

Find the z-score for 48 given a mean of 50 and a standard deviation of 5.

• 2.5

• -2.5

• -0.4

• 0.4

Tags

CCSS.HSS.ID.A.4

Find the z-score for 258 given a mean of 273 and a standard deviation of 5.

• 3

• -2

• 2

• -3

Tags

CCSS.HSS.ID.A.4

When Easton runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 3 seconds. Using the empirical rule, determine the interval of times that represents the middle 68% of his finishing times in the 400 meter race.

• (73, 88)

• (77, 88)

• (77, 83)

• (76, 86)

IQ tests have a mean of 100 and SD of 16. Einstein's IQ was 160. What is the z-score of his IQ?

• 1.75

• 3.75

• 0.75

• 2.75

Tags

CCSS.HSS.ID.A.4

Z-score of 2.5 on an IQ test is considered a genius (mean=100, SD=16). What score makes someone a genius? Hint: SOLVE for X

• 89.2

• 130

• 99.38

• 140

Tags

CCSS.HSS.ID.A.4

The mean GPA of students in a course at UGA is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8?

• 81.9%

• 47.5%

• 68%

• 95%

​ The monthly income of 5000 workers at the Microsoft plant are distributed normally. Suppose the mean monthly income is $1250 and the standard deviation is $250.

Creating a normal distribution curve shows that the amount of workers who earn less than $750 per month is ​ (a)  

• 800 workers
• 125 workers
• 81.5% of workers
• 97.5% of workers

A set of middle school student heights are normally distributed with a mean of  150 centimeters and a standard deviation of  20 centimeters. Find the probability of randomly selecting a student that is 115 cm or less?

• 0.04

• 4%

• 0.05

• 5%