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# The Beanstalk Club

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Please see attachment for full problem description. I need help with figuring out probability and normal distribution problems.

For the following problems, determine whether a probability distribution is given. In those cases where a probability distribution is not described, identify the requirements that are not satisfied. In those cases where a probability distribution is described, find its mean and standard distribution.

#1 Three males with an X linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the x linked genetic disorder.

x P(x)
0 0.4219
1 0.4219
2 0.1406
3 0.0156

#2 A researcher reports that when groups of four children are randomly selected from a population of couples meeting certain criteria, the probability distribution for the number of girls is as given in the accompanying table.

x P(x)
0 0.502
1 0.365
2 0.098
3 0.011
4 0.001

#3 A genetics experiment involves offspring peas in groups of four. A researcher reports that for one group, the number of peas with white flowers has a probability distribution as given in the accompanying table.

x P(x)
0 0.04
1 0.16
2 0.80
3 0.16
4 0.04

In the following exercises assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15.

Find the probability that a randomly selected adult has an IQ that is less than 130.

Find the probability that a randomly selected adult has an IQ between 90 and 110.

Find P10, which is the IQ score separating the bottom 60% from the top 40%.

In the following exercise use the following information:
Men's heights are normally distributed with mean 69.0 inches and dtandard deviation 2.8 inches.
Women's heights are normally distributed with mean 63.6 inches and standard deviation 2.5 inches.

1. The Beanstalk Club, a social organization for tall people, has a requirement that women must be at least 70 inches tall. What percentage of women meet that requirement?

Birth weights in the United States are normally are normally distributed with a mean of 3420 grams and a standard deviation of 495 grams. If a hospital plans to set up special observation conditions for the lightest 2% of babies, what weight is used for the cut off separating the lightest 2% from the others?

Birth weights in Norway are normally distributed with a mean of 3570 grams and a standard deviation of 500 grams. Repeat the previous exercise for babies born in Norway. Is the result very different?