AP StatisticsName: ______

Section 6.1 Worksheet

1. Suppose you roll a pair of fair, six-sided dice. Let T = the sum of the spots showing on the up-faces.

a) Find the probability distribution of T.

b) Find P(T ≥ 5) and interpret the result.

This means that about five-sixths of the time, when you roll a pair of 6-sided dice, you will have a sum of 5 or more.

2. In 2010, there were 1319 games played in the National Hockey League’s regular season (Don’t forget that the Blackhawks won it all though!!!!). Imagine selecting one of these games at random and then randomly selecting one of the two teams that played in the game. Define the random variable X = number of goals scored by a randomly selected team in a randomly selected game. The table below gives the probability distribution of X:

a) What is the probability that the number of goals scored by a randomly selected team in a randomly selected game is at least 6?

P(X≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.041 + 0.015 + 0.004 + 0.001 = 0.061.

b) Compute the mean of the random variable X and interpret this value in context.

= 2.851. The mean number of goals for a randomly selected team in a randomly selected game is 2.851. If you were to repeat the random sampling process over and over again, the mean number of goals scored would be about 2.851 in the long run.

c) Compute the standard deviation of the random variable X and interpret this value in context.

The standard deviation of X is 1.632. The number of goals scored by a randomly selected team typically varies by about 1.6 goals from the mean, 2.851.

3. In government data a household consists of all occupants in a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States:

Number of persons
1 / 2 / 3 / 4 / 5 / 6 / 7
Household Probability / 0.25 / 0.32 / 0.17 / 0.15 / 0.07 / 0.03 / 0.01
Family Probability / 0 / 0.42 / 0.23 / 0.21 / 0.09 / 0.03 / 0.02

a) Fill in the missing values for 7 persons

b) Calculate and interpret the mean for each probability distribution. Explain the difference in the two means.

Household 2.6 peopleThe number of people in a randomly selected household is expected to be about 2.6 people.

Family 3.14 people The number of people in a randomly selected household is expected to be about 3.14 people.

The family mean is higher because there are no values equal to 1 in the family distribution, but a value of 1 is very common in the household distribution

d) Calculate and interpret the standard deviation for each probability distribution.

Household = 1.421. The number of people in a randomly selected household will typically differ from the mean of 2.6 by about 1.421 people.

Family = 1.249. The number of people in a randomly selected family will typically differ from the mean of 3.14 by about 1.249 people.

4. The Iowa Test of Basic Skills is a standardized test given to all 7th graders in the state of Iowa. The distribution of scores is approximately normal with and Find the probability of a student getting a score higher than 9. Show all work!

Let X = the score of a randomly chosen 7th grader.

We are finding P(X 9)

P(X 9) = normalcdf (lower = 9, upper = 1E99, = 6.8, = 1.6) = 0.0846

There is an 8.46% chance of selecting a student with a score higher than 9.

5. The GPA (grade point average) of students who take the AP Statistics exam are approximately normally distributed with a mean of

3.4 and a standard deviation of 0.3. What is the probability that a student selected at random from this group has a GPA lower than

3.0? Round to four decimal places.

Let X = the GPA of a randomly chosen AP Statistics student.

We are finding P(X3.0)

P(X3.0)= normalcdf (lower = -1E99, upper = 3.0, = 3.4, =0 .3) = 0.0912

There is a 9.12% chance of selecting an AP Statistics student with a GPA lower than 3.0.