Using Standard Deviation
Z-Scores
Probabilities and Percentages
100

Find the standard deviation of the following sample of scores on a 100-point quiz: 34, 45, 55, 56, 62, 75, 77, 85, 98, 100.

22.04

100
Mr. Hessler timed all of his ski runs down the mountain last weekend and found that his average time down the mountain was 250 seconds with a standard deviation 24 seconds. He crashed on one run, and it took him 314 seconds to make it down the mountain. What is the z-score of that run?

z=2.67

100

The mean length of time Mr. Hessler's students spend studying per week is 25 minutes with a standard deviation of 11 minutes. His star student studies 50 minutes per week. What percent of students study less than his star student?

98.8%

200

A z-score of -2 means that I am _____ (how many?) standard deviaton(s) _____ (above/below) the mean.

2; below

200

LeBron James has averaged 29.9 points per game this month with a standard deviation of 8.15 points. He scored 40 points against Portland last Thursday night. What is the z-score associated with that game?

z=1.24

200

The high temperature in Greeley on February 18 was 10 degrees. The average high temperature for the date is 51 degrees with a standard deviation of 12 degrees. What percent of February 18s would be expected to have temperatures warmer than this year's February 18? Round the percentage to two decimal places.

99.97%

300

If the smallest observation is removed from a data set, the mean will ___________ (increase/decrease/stay the same), and the standard deviation will _________ (increase/decrease/stay the same).

increase; decrease

300

The average age of US Presidents when elected is 56.0 years with a standard deviation of 7.9 years. Donald Trump was the oldest person ever elected at 78.6 years old. What is the z-score associated with President Trump's age?

z=2.86

300

The average length of a Beatles song is 164.0 seconds with a standard deviation of 45.3 seconds. What percentage of Beatles songs were between 2 and 3 minutes in length?

47.08%

400
Draw a normal curve for data with a mean of 16 and standard deviation of 2.5. Fill in the corresponding values for z-scores of -3, -2, -1, 0, 1, 2, and 3.

Values should be 8.5, 11, 13.5, 16, 18.5, 21, 23.5

400

The average length of a Top 10 song on the Billboard 100 in 2024 was 3 minutes 40 seconds with a standard deviation of 27 seconds. Kendrick Lamar's hit "They Not Like Us" had a run time of 4 minutes 34 seconds. Find the z-score associated with "They Not Like Us."

2

400

The average 40-yard dash time of NFL wide receivers is 4.48 seconds with a standard deviation of .09 seconds. Mr. Sibley ran a 40-yard dash in 4.35 seconds. What percentage of NFL wide receivers ran a 40-yard dash time slower than Sibley?

92.5%

500

Data on number of birds to land on a pond on any given day are normally distributed with a mean of 74 and a standard deviation of 6.3. Which of the following observation(s) would be considered outliers? 

a. 55

b. 57

c. 85

d. 92

a.

500

The cast of Legally Blonde asked me to do some research for them. I found that the average length of a song on the Legally Blonde Spotify playlist is 249 seconds with standard deviation of 124 seconds. What song length would be the 75th percentile?

332 seconds

500

Last week, the GCHS bowlers averaged 146 with a standard deviation of 31. Ms. Watson scored in the 36th percentile one of her games. What was her score that game?

135

M
e
n
u