Question

4.4.12 How many ways can you choose seven people from a group of twenty?

5.1.2 Suppose you have an experiment where you flip a coin three times. You then count the number of heads. State the random variable. Write the probability distribution for the number of heads. Draw a histogram for the number of heads. Find the mean number of heads. Find the variance for the number of heads. Find the standard deviation for the number of heads. Find the probability of having two or more number of heads. Is it unusual to flip two heads?

5.1.4 An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warranty costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?

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.) b.) c.) d.) e.) f.)

5.2.10 The proportion of brown M&M’s in a milk chocolate packet is approximately 14% (Madison, 2013). Suppose a package of M&M’s typically contains 52 M&M’s. State the random variable. Argue that this is a binomial experiment Find the probability that Six M&M’s are brown. Twenty-five M&M’s are brown. All of the M&M’s are brown. Would it be unusual for a package to have only brown M&M’s? If this were to happen, what would you think is the reason?

5.3.4 Approximately 10% of all people are left-handed. Consider a grouping of fifteen people. State the random variable. Write the probability distribution. Draw a histogram. Describe the shape of the histogram. Find the mean. Find the variance. Find the standard deviation.

Answer 1

(4.4.12)

7 people can be chosen from a group of 20 in C(20, 7) ways = 77520 ways

(5.1.2)

Random variable is x = number of heads in 3 flips of a coin

S = {hhh, hht, hth, htt, ttt, tth, tht, thh}

Probability distribution:

x	P(x)
0	0.125
1	0.375
2	0.375
3	0.125

Histogram:

x	Frequency	P(x)	x P(x)	x^2 P(x)
0	1	0.125	0	0
1	3	0.375	0.375	0.375
2	3	0.375	0.75	3
3	1	0.125	0.375	3.375
	Mean, μ = ∑x P(x) = 1.5
	Variance = ∑x^2 P(x) - μ^2 = 6.75 - 1.5^2 = 4.5
	Standard deviation, σ = √4.5 = 2.12

P(2 or more heads) = 0.375 + 0.125 = 0.5. This is not unusual.

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