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# Probability based on normal and binomial variable

Question 6
A manager must select 2 people from a list of 13 specialized employees to form a special group. In how many ways can the manager choose to select 2 people? [Hint: Fundamental counting principle]

Question 7
57% of families say that their children have an influence on their vacation destinations. Consider a random sample of six families who are asked if their children have an influence on their vacation destination. [Hint: Binomial probability; see example 3 of page 187]
a. Construct a binomial distribution.
b. Find the mean, variance and standard deviation of the distribution.

Question 8
The probability that an individual is left-handed is 0.1. In a class of 30 students, what is the probability of finding at least five left-handers? [Hint: Binomial probability; P(at least 5)=1-{P(0)+P(1)+P(3)+P(4)}]
a. Construct a binomial distribution.
b. Find the mean, variance and standard deviation of the distribution

Question 9
Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normal probability using the continuity correction.
Binomial Probability Normal Probability
c. P ( x â?¤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ? )

Question 10
The world?s smallest mammal is the Kitti?s hog-nosed bat, with a mean weight of 1.5 grams and a standard deviation of 0.25 grams. Assuming that the weights are normally distributed, find the probability of randomly selecting a bat that weighs
a. Between 1.0 grams and 2.0 grams.
b. Between 1.6 grams and 2.2 grams.
c. More than 2.2 grams.

#### Solution Summary

The solution gives the complete steps of calculation of probability, mean, variance and standard deviation for normal and binomial random variable.

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