UI STAT 251 Spring 2011
Quiz 2
NAME:
UI #:
1. (1 point) What is the meaning of having a z-score equals to -2.17? Explain in your own words.
It means that the observation lies 2.17 standard deviation below the mean.
2. (1 point) For a normal distribution, what proportion of observations will lie more than 1.2 standard deviation above
the mean?
> 1-pnorm(1.2)
[1] 0.1150697
About 11.5% of observations will lie more than 1.2 standard deviation above the mean.
3. (2 points) For a normal distribution, what is the 75-th percentile located in terms of z-score? What about the 85-th
percentile?
> qnorm(.75)
[1] 0.6744898
> qnorm(.85)
[1] 1.036433
75-th percentile located 0.67 standard deviation above the mean and 85-th percentile located 1.04 standard deviation above
the mean.
4. (6 points) The height of men is known to be normally distributed with mean 70 inches and standard deviation 2.5
inches.
a) What percent of men are taller than 68 inches?
> z=(68-70)/2.5
> 1-pnorm(z)
[1] 0.7881446
b) What percent of women are between 68 and 71 inches tall?
> z1=(71-70)/2.5
> z2=(68-70)/2.5
> pnorm(z1)-pnorm(z2)
[1] 0.4435663
c) What are the values of the Q1 and Q3 for the height of women?
> 70+qnorm(c(.25,.75))*2.5
[1] 68.31378 71.68622