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WorksheetsZ-Scores and Z-Score Table Quiz
Total questions: 30
Worksheet time: 3600secs
The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5. What proportion of weeks would you expect to have less than 5 accidents?
Hint: Find z-score, then look up z-score in table
0.6915
0.1762
0.8238
-0.93
The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the z-score for a player who runs a time of 5.6 seconds?
-1.33
1.33
0.88
1.02
The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.
If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?
Hint: Find z-score then look up z-score in table and convert to a percent
92.4%
10.5%
16%
7.6%
The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.
Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?
Hint: Work backwards...convert percent to a decimal and find decimal in z-score table chart to get z-score and then use z-score to find IQ value
115
130.75
145
120
The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.
Suppose a male long jumper's jump ranked in the 75th percentile. How long was his jump?
Hint: work backwards... change percentile to decimal and find within z-score chart to find z-score and then convert z-score to long jump distance
0.67 inch
263 inches
272.44 inches
277.25 inches
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.
About what percent of the products last between 12 and 15 days?
Hint: Find the z-score of each value, subtract and look up value in z-score table and convert to percent or use empirical rule
68%
34%
16%
2.5%
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
Find the percent under the standard normal curve that lies to the left of z=2.1.
Hint: Use z-score table and convert to percent
1.79%
-1.79%
98.21%
0.98%
Find the percent under the standard normal curve that lies to the right of z=-0.67.
Hint: find the value in the z-score table and convert to %
63.42%
74.86%
25.14%
50%
A test has a mean of 40 and a standard deviation of 10. What is the percent of people that scored above 62?
Hint: Find the z-score and look up the value in the z-score table and convert to a percent
1.39%
45.34%
98.41%
22.34%
A continuous random variable is normally distributed with mean 145 and standard deviation is 5. Find P(136<X<140).
Hint: Find the z-scores for each value and look up in the z-score table then subtract values
0.8054
0.8772
0.1228
0.1587
Find the z-score for 258 given a mean of 273 and a standard deviation of 5.
3
2
-2
-3
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
Mean=11, SD=30. Find the raw score (X) for z=-1.5
Hint: work the z-score formula backwards
35
45
55
65
The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the z-score for a player who runs a time of 5.6 seconds?
-1.33
1.33
.88
1.02
The monthly phone bills in a city are normally distributed with a mean of 30$ and a standard deviation of 12$. Find the x-value that correspond to z-scores of 3.17.
$1.80
$68.04
$32.76
$42.80
Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in. Assuming a normal distribution, find the percentage of men meeting this requirement if the mean height of men is 68.6 inches and the standard deviation is 2.8 inches.
0.0092%
9.2 %
9.2 %
0.92%
Assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability of a score greater than -2.93.
-0.0017
-0.9983
0.0017
0.9983
Books in the library are found to have average length of 350 pages with standard deviation of 100 pages, and follow a normal distribution. What is the probability that a randomly selected book will be 80 pages or less?
.0032
.0035
.9965
.4965
Find the area under the standard normal curve where z < 2.42
.008
.992
.301
.862
Find the area to the right of z= -1.02
.846
.782
.154
.523
The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. How many standard deviations from the mean would a temperature of 17 degrees be?
1
1.429
-1.429
11.5
The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. Approximately what percent of days in February will have days below 23 degrees?
5%
34%
50%
68%
The average height of NBA basketball players is 79 inches with a standard deviation of 1.75 inches. Approximately what percent of the players are taller than 82 inches?
about 4% to 5%
about 2% to 3%
about 6% to 7%
On a science test, a score of 91 falls exactly 1.5 standard deviations above the mean. If the standard deviation for the test is 8, what is the mean score?
79
75
72
81
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with mean of 1497
and standard deviation of 322. Calculate the z-score of a student earning a score of 1980.
2
1.75
1.5
2.25
Which is better, a z-score of 1.2 or a z-score of -2.1?
1.2 because it's bigger
1.2 because it's listed first
-2.1 because it's bigger
-2.1 because it's listed second
A z-score of 1.25 is greater than what percent of data?
.8944
89.4
89.44
89.44%
Which histogram below most closely depicts a normal distribution?
The Breakfast cereal Company packcereal in bags marked as 250 g
A large number of packs ofcereal were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.
Assuming this data is normally distributed, what percentage of packs are underweight?
2.5.%
3.5%
4%
5%
