# Samples, Bias, & Survey Design

```AP STATISTICS
Quiz-6.1 Discrete and Continuous Random Variables
Last 4 of Student ID____________
Period______
1. Imagine selecting a U.S. high school student at random. Define the random variable X=number of languages spoken by the randomly
selected student. The table below gives the probability distribution of X, based on a sample of students from the U.S. Census at School
database:
Languages:
1
2
3
4
5
Probability:
0.630
0.295
0.065
0.008
0.002
(a) Is this a legitimate probability distribution? Explain how you know.
Yes, since the probabilities add to 1.
(b) Make a histogram of the probability distribution. Describe what you see.
Center: Median=1
Unusual Features: There are outliers above 3.5 (4&amp;5)
Shape: Skewed Right
Spread: Range-5 – 1 = 4 and IQR-2 – 1 = 1
(c) What is the probability that a randomly selected student speaks at least three languages?
P(X≥3)=0.065+0.008+0.002=0.075
(d) Compute the mean of the random variable X and interpret this value in context.
&micro;X=the mean number of languages spoken by U. S. high school students in the long run=1.457
(e) Compute and interpret the standard deviation of the random variable X.
𝝈X=the typical distance from the mean (1.457) for each U. S. high school student=0.6709
2. The weight of 3-year-old females closely follow a Normal distribution with a mean of &micro;=30.7 pounds and a standard deviation of 3.6
pounds.
(a) What is the probability that a randomly selected 3-year-old female weighs at least 30 pounds?
P(X≥30) normalcdf(30,100,30.7,3.6)=0.577
(b) What is the probability that a randomly selected 3-year-old female weighs less than 30 pounds?
P(X&lt;30) normalcdf(0,30,30.7,3.6)=0.423
(c) What is the probability that a randomly selected 3-year-old female weighs between 25 and 35 pounds?
P(25&lt;X&lt;35) normalcdf(25,35,30.7,3.6)=0.827
```