# Binomial, Poisson, Normal Distribution; Confidence Intervals

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Binomial Distribution

Determine whether or not the given procedure results in a binomial distribution.

1. Twenty different students are randomly selected from those attending a private boys school and asked whether he or she is traveling over the Christmas holidays.

2. A six-sided die is rolled 40 times and the results are recorded.

Answer the following questions using the binomial distribution.

3. The brand name of McDonald's has a 95% recognition rate (based on data from Retail

Marketing Group). If a McDonald's executive wants to verify that rate by beginning with a

small sample of 15 randomly selected consumers, find the probability that exactly 14 of the 15

consumers recognize the McDonald's brand name.

4. Random guesses are made for 50 SAT multiple choice questions, so n=50 and p=0.2 .

Find the number of correct answers that can be expected .

Poisson Distribution

State two of the four requirements for the Poisson Distribution.

Normal Distribution

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. A letter was written to "Dear Abby" in which a wife claimed to have given birth 308 days after a brief visit from her husband who was serving in the Navy.

1. Find the probability of a pregnancy lasting 308 days or longer.

2. What does this result suggest?

We stipulate that a baby is premature if the length of the pregnancy is in the lowest 4%.

3. Would a baby who is born at 215 days be considered premature?

4. Find the length of pregnancy that separates premature babies from those who are not premature

Student t Distribution - Confidence Intervals

A simple random sample of the body temperatures of 106 healthy humans were taken for which

x=98.20o F and s=0.62oF .

1. What two requirements must be satisfied to use a Student t distribution.

2. Determine the number of degrees of freedom for this sample size.

3. Construct a 99% confidence interval to estimate the mean body temperature of all healthy humans.

4. What does the confidence interval suggest about the use of 98.6o as the mean body

temperature.

https://brainmass.com/statistics/probability/binomial-poisson-normal-distribution-confidence-intervals-365153

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Binomial Distribution

Determine whether or not the given procedure results in a binomial distribution.

1. Twenty different students are randomly selected from those attending a private boys school and asked whether he or she is traveling over the Christmas holidays.

Since the students are selected without replacement from a small population, the trials are not independent and the probability of success will differ with each trial. So the procedure does not result in a binomial distribution.

2. A six-sided die is rolled 40 times and the results are recorded.

Since we have six different outcomes for each trial, the procedure does not result in a binomial distribution. We would have to define success and failure (for example, success="rolling a 6" and failure="not rolling a 6") for this experiment in order to have a binomial ...

#### Solution Summary

Binomial, Poisson, Normal distribution and confidence intervals are examined.

Poisson distribution Confidence Interval

Solve the following problem:

Find 95% confidence intervals for the population percent dying based on these data: (1) 199 of 13,078 electronics technicians died of disease; (2) 100 of 13,078 electronics technicians died of circulatory disease; (3) 308 of 10,116 radarmen died (of any cause); (4) 441 of 13,078 electronics technicians died (of any cause); (5) 103 of 10,116 radarmen died of an accidental death.

(a) Use the normal approximation to the Poisson distribution (which is approximating a binomial distribution).

(b) Use the large-sample binomial confidence intervals (of Section 6.2.6). Do you think the intervals are similar to those calculated in part (a)?