3, it is believed to be true that 15% of the US. population is left-handed. You

Question

3, it is believed to be true that 15% of the US. population is left-handed. You randomly select 10 people. Let x represent the number of left-handers. Construct a binomial distribution. What calculator function and inputs did you use? a. (Show 3 decimal places or as many as it takes to get to one non-zero digit.) b. c. d. e. (b-d) State answers using mathematical notation. Find the probability that exactly 8 people are left-handed. Find the probability that less than 3 people are left-handed. Find the probability that at least 1 person is left-handed. Find the mean and standard deviation of the binomial distribution. (Show your work and answer as a sentence.) vour naner and fill in the blanks (from #2 above):

Explanation / Answer

A) p = 0.15

n = 10

P(X = x) = 10Cx * 0.15x * (1-0.15)10-x

B) P(X = 8) = 10C8 * 0.158 * 0.852 = 0.000

C) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= 10C0 * 0.150 * 0.8510 + 10C1 * 0.151 * 0.859 + 10C2 * 0.152 * 0.858

= 0.820

D) P(X > 1) = 1 - P(X = 0)

= 1 - 10C0 * 0.150 * 0.8510

= 1 - 0.197

= 0.803

E) mean = n * p = 10 * 0.15 = 1.5

Standard deviation = sqrt (n * p* (1-p)) = sqrt (10 * 0.15 * 0.85) = 1.129

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