Finding Proportions
Find the proportion of observations from a Standard Normal distribution if z<-1.18
Round at least 2 places past the decimal (hundredths or thousandths)
0.119
Suppose the following heights in inches is N(64.6, 2.15). What is the z-score of someone who is 68 inches? Round to the nearest hundredth.
1.58
Suppose the distribution of heights in inches is N(66.4, 2.89). At what height is the 10th percentile? Round to the nearest hundredth.
62.70
She is taller than 10% of people.
Or 10% of people are shorter than her.
Suppose the 20th percentile of heights is 63.4 inches and the 80th percentile is 70.2. What is the mean of this distribution?
66.8 inches
Find the proportion of observations from a Standard Normal distribution if -2.05<z<2.08
Round at least 2 places past the decimal (hundredths or thousandths)
0.961
Suppose the following heights in inches is N(64.6, 2.15). What is the z-score of someone who is 52 inches? Round to the nearest hundredth.
-5.86
Suppose the distribution of heights in inches is N(66.4, 2.89). At what height is the 90th percentile? Round to the nearest hundredth.
70.10 inches
What is a z-score?
It tells you how many standard deviations above or below the mean you are.
Suppose the 20th percentile of heights is 63.4 inches and the 80th percentile is 70.2. What is the standard deviation of this distribution?
SD = 4.04
Rounding might be off
Suppose the following heights in inches is N(64.6, 2.15). Find the probability that someone is taller than 68 inches.
Round to the nearest hundredth or thousandth.
0.057
Someone is in the 20th percentile in their class in terms of height. What is their z-score? Round to the nearest hundredth.
-0.84
Suppose the distribution of heights in inches is N(66.4, 2.89). How tall do you have to be to be in the top 20th percentile? Round to the nearest hundredth.
68.83
A person's height is 63 inches and in this distribution, this yields a z-score of -2.1. Interpret the z-score in this context.
She is 2.1 standard deviations below the mean.
Or: Her height is 2.1 standard deviations below the mean.
Suppose the 73rd percentile of heights is 68.3 inches and the 27th percentile is 62.1. What is the standard deviation of this distribution?
Round to the nearest hundredth. Show all work.
SD: 5.06 (rounding might be slightly off)
Suppose the following heights in inches is N(64.6, 2.15). Find the probability that someone is between 62.5 and 72.1 inches.
Round to the nearest hundredth or thousandth.
0.835
Someone is in the 99th percentile in their class in terms of height. What is their z-score? Round to the nearest hundredth.
2.33
Suppose the distribution of heights in inches is N(66.4, 2.89). At what heights are the middle 80th percentile?
62.70 and 70.10 inches
Suppose you surveyed 15 people. 3 are 62 inches, 4 are 69 inches, and 8 are 66 inches. Interpret the percentile of someone who is 66 inches.
Suppose the 3rd percentile of heights is 59.55 inches and the 87th percentile is 65.87 What is the mean of this distribution?
Round to the nearest hundredth. Show all work.
Mean = 63.5
Rounding might be a bit off.
Suppose the following heights in inches is N(64.6, 2.15). Find the probability that someone is shorter than 50 inches.
Round to the nearest hundredth or thousandth.
Someone is in the 22th percentile in their class in terms of height. Another person is in the 81st percentile. What are their z-scores? Round to the nearest hundredth.
-0.77 and 0.88
Suppose the distribution of heights in inches is N(66.4, 2.89). At what heights are the middle 60th percentile?
63.97 and 68.83 inches
Suppose the distribution of heights in inches is N(66.4, 2.89). Interpret the percentile of someone who is 67 inches.
Probability is 0.5822 which means they are taller than 58.22% of people in this distribution.
Suppose the 3rd percentile of heights is 59.55 inches and the 87th percentile is 65.87 What is the standard deviation of this distribution?
Round to the nearest hundredth. Show all work.
SD = 2.1
Rounding might a bit off.