# Population Sample Data, Binomial & Normal Distributions

1. Why do we want to assume that our sample data represent a population

distribution?

2. What are the differences between the binomial and normal distributions?

Thank you.

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#### Solution Preview

PLEASE SEE RESPONSE ATTACHED (ALSO PRESENTED BELOW), INCLUDING ONE SUPPORTING ARTICLE. I HOPE THIS HELPS AND TAKE CARE.

RESPONSE:

1. Why do we want to assume that our sample data represent a population distribution?

We want to assume our sample represents a population distribution because we want to generalize our findings to the population. For example, if we researched a sample (N=30) of organizations and found that the team approach to management is more effective than authoritarian management style, we would want to conclude that this is true for all organizations (i.e., population). In order to do this, we must assume that our sample (N=30) is representative of the population of all organizations.

2. What are the differences between the binomial and normal distributions?

The main differences between the two distributions are in their location and scale parameters (mean and standard deviations) and in the overall shape of the distribution (bell-shaped versus not bell-shaped). Let's take a closer look at the two distributions.

a. Normal distributions are symmetrical and have a bell-shaped distribution.

The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. It is a ...

#### Solution Summary

This solution discusses normal distribution and why we want to assume that our sample data represent a population distribution. The differences between the binomial and normal distributions are also discussed. Many examples are provided as well as one supporting article for further reading.

Binomial, Poisson, Normal Distribution; Confidence Intervals

See attached file.

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.