STAT 200 Week 3 Homework Solutions

#1 4.2.2

Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. Table #4.2.2 gives the defect and the number of defects.

Table #4.2.2: Number of Defective Lenses

a.) Find the probability of picking a lens that is scratched or flaked. (5 pts)

b.) Find the probability of picking a lens that is not the wrong shape.(5 pts)

#2 4.4.6 Find 10P6 (5 pts)

3 4.4.12 How many ways can you choose seven people from a group of twenty?(5 pts)

#4 5.1.2

Suppose you have an experiment where you flip a coin three times. You then count the number of heads.

a.) State the random variable. (5 pts)

b.) Write the probability distribution for the number of heads. (5 pts)

c.) Draw a histogram for the number of heads.Include a descriptive title and axes titles. (5 pts)

d.) Find the expected number of heads (5 pts) and the variance (5 pts)

e.) Find the standard deviation for the number of heads. (5 pts)

f.) Find the probability of having two or more heads. (5 pts)

g.) Is it unusual to flip two heads?(5 pts)

#5 5.2.4

Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using technology.

a) P(x=1) (2 pts)

b) P(x=3) (2 pts)

c) P(x ≤ 3) (2 pts)

d) P(x ≥ 5) (2 pts)

e) P(x ≤ 4) (2 pts)

#6 5.3.4

Approximately 10% of all people are left-handed. Consider a grouping of fifteen people.

n = 15 and p = 0.10

a) State the random variable. (5 pts)

b) Write the probability distribution. (5 pts)

c) Draw a histogram. Include a descriptive title and axes titles. (5 pts)

d) Describe the shape of the histogram. Discuss any outliers. Provide your answer as a complete sentence.(5 pts)

e) Find the mean.(5 pts)

f) Find the standard deviation.(5 pts)