# Calculate probability under either binomial or normal distribution

All problems are to be computed by hand with work shown; type your work up in word.

Question 1: The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with a mean of 266 days and standard deviation of 16 days.

•What percent of pregnancies last less than 240 days?

•What percent of pregnancies last between 240 days and 270 days?

•How long do the longest 20% of pregnancies last?

Question 2: A federal report find that a lie detector test given to truthful persons have a probability of 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants to take a lie detect test. Suppose that all 12 applicants answer truthfully.

•What is the probability that exactly one is being deceptive.

•What is the probability that at most one is being deceptive.

•What is the mean and standard deviation of this distribution.

https://brainmass.com/statistics/probability-theory/calculate-probability-under-either-binomial-normal-distribution-596647

#### Solution Summary

The solution gives detailed steps on calculating probability under either binomial or normal distribution.

This problem shows how to calculate probabilities and percentiles from normal and binomial probability distributions.

A company that sells annutities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

A company that sells annuitites must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and and a standard deviation of 3.5 years. What proportion of the plan recipients would recieve payments beyond age 75?

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of american hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability of all the hotels in the sample that offer hairdryers in the bathrooms.

A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of american hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled between 16 and 21 minutes.

A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?

0.0256

0.0625

0.16

1.00