Name: ______Date: ______

STATS REVIEW- CH.4 Probability Distributions

1.  Decide whether the following is a probability distribution:

a.

x / 0 / 1 / 2 / 3 / 4
P(x) / 0.36 / 0.23 / 0.08 / 0.14 / 0.29
x / 1 / 2 / 3 / 4 / 5 / 6
P(x) / 0.05 / 0.15 / 0.40 / 0.25 / 0.10 / 0.05

b.

2.  Decide whether the random variable x is discrete or continuous:

a)  x represents the weight of a truck at a weigh station

b)  x represents the number of people interested in studying art.

3.  During a one-year selling period, a sales representative made between 0 and 5 sales per day, as shown in the table. If this pattern continues what is the expected value for the number of sales per day? Standard deviation?

Number of Sales, x / Frequency, f (in days)
0 / 25
1 / 43
2 / 60
3 / 42
4 / 20
5 / 10

4.  The results of a survey state that 41% of people prefer dogs to any other pet. You randomly select 5 people who participated in the survey. Let x represent the number of people who prefer dogs.

a)  Construct a binomial distribution

b)  Find the probability that exactly two people prefer dogs.

c)  Find the probability that less than 4 people prefer dogs.

d)  Find the mean of the binomial distribution.

e)  Find the standard deviation of the binomial distribution.

f)  Graph a histogram and describe the shape

g)  What values of x would you consider unusual?

h)  Interpret

Decide if the following are geometric, poisson or binomial distributions. Solve.

5.  An auto parts seller finds that 1 in every 100 parts sold is defective. Find

the probability that

a) the first defective part is the tenth part sold

b) first defective part is the first, second, or third part sold

6.  One in five people in the US own individual stocks. In a random sample of 12 people, what is the probability that the number owning individual stocks is:

a)  Exactly 4

b)  At least 4

c)  More than 4

7.  A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century the mean number of major hurricanes to strike the US mainland per year was about 0.7. Find the probability that in a given year

a)  2 major hurricanes will strike the US mainland.

b)  1 major hurricane will strike the US mainland

8.  The mean number of days with 0.01 inches or more precipitation per month for Allendale, New Jersey is about 8.7. Find the probability that in a given month there are 9 days with 0.01 inches or more precipitation.

9.  One in four adults is currently on a diet. In a random sample of eight adults, what is the probability that the number currently on a diet is

a)  exactly 3

b)  at least 3

c)  more than 3

10.  A cereal maker places a game piece in its cereal boxes. The probability of winning a prize in the game is 1 in 4. Find the probability that you:

a)  Win your first prize with your fourth purchase

b)  Win your first prize with your first, second, or third purchase