Binomial and Normal Distributions

1. Suppose that you counted the number of boys and girls among the children of each family in your village. Suppose further that we categorize a child either as a boy or girl only.

You estimated the probability that a child is a boy as 0.51. Estimate the probability that a child is a girl.

2. Suppose that you counted the number of boys and girls among the children of each family in your village. Suppose further that we categorize a child either as a boy or girl only.

You estimated the probability that a child is a boy as 0.35. Compute the standard deviation for counting the number of girls in a family in this village assuming there were 22 children.

3. Suppose that you counted the number of boys and girls among the children of each family in your village. Suppose further that we categorize a child either as a boy or girl only.

You estimated the probability that a child is a boy as 0.53.What is the probability that in a family of 6 children, 4 will be boys?

4. Suppose that you counted the number of boys and girls among the children of each family in your village. Suppose further that we categorize a child either as a boy or girl only.

You estimated the probability that a child is a boy as 0.59.What is the probability that in a family of 4 children, at least two are girls?

5. Suppose that you counted the number of boys and girls among the children of each family in your village. Suppose further that we categorize a child either as a boy or girl only.

You estimated the probability that a child is a boy as 0.64. What is the probability that in a family of 5 children, there is at least 1 boy?

6. A soft-drink machine can be regulated so that it discharges an average of ounces per cup.

If the ounces of fill are normally distributed with a standard deviation 0.26 ounces, give the setting for so that 10-ounce cups will overflow only 1% of the time.

7. A soft-drink machine can be regulated so that it discharges an average of ounces per cup.

If the machine has a standard deviation that can be fixed at certain levels by carefully adjusting the machine, what is the largest value of that will allow the actual amount dispensed to fall within 0.54 ounces of the mean with a probability of at least 0.95?