# Normal, Binomial, Probability, Confidence interval

16) If the random variable z is the standard normal distribution, then z(0.2324) =

23) Determine the minimum number of subjects to be polled for a survey with a margin of error of six percentage points and a confidence level of 95%

a.253 b.267 c.278 d.306 e.none of these

32) Samples of size 10 are selected from a normal population with a mean of 35.5 and a standard deviation of 6.5. For the population find P(29.5<x<40.0)

33) A certain population has a bimodal distribution with a mean of 58.5 and a standard deviation of 2.5. Many samples of size 25 are randomly selected and their means calculated. What value would you expect to find for the standard deviation of the sample mean?

34) When estimating a population mean with a confidence interval estimate, then E is:

a. equal to the level of confidence.

b. one-half the width of the confidence interval.

c. a multiples of the population mean

d. a multiple of the population standard deviation

e. none of these

35) Suppose you selected 200 different samples from a large population and used each sample to construct a 0.95 confidence interval estimate for the population mean. How many of the 200 confidence interval estimate should you expect to actually contain the population mean M?

36) You are constructing a 95% confidence interval using the information: n=60, x=65.5, s=2.5, and E=0.7. What is the value of the middle interval?

37) Several students are unprepared for a multiple choice quiz with 10 questions. All of their answers are guesses. Each question has five possible answers and only one is correct. What is the standard deviation of this distribution?

38) Ten percent of American adults are left-handed. A statistical class has 25 students. Find the mean number of left-handed students in such classes of 25 students.

39) Which of the following is not a requirement for a binomial distribution?

a.The procedure has a fixed number of trials.

b.The trials must be dependant.

c. Each trial must have all outcomes classified in two categories

d. The probabilities must remain constant for each trial

e. none of these

40) Is the experiment of spinning a roulette wheel a binomial experiment? Y/N

© BrainMass Inc. brainmass.com October 16, 2018, 5:08 pm ad1c9bdddfhttps://brainmass.com/statistics/confidence-interval/normal-binomial-probability-confidence-interval-45304

#### Solution Preview

16) If the random variable z is the standard normal distribution, then z(0.2324) =

Cumulative probability=0.2324

Therefore Z(0.2324)=-0.7310

(from the tables or using EXCEL function NORMSINV)

23) Determine the minimum number of subjects to be polled for a survey with a margin of error of six percentage points and a confidence level of 95%

a.253 b.267 c.278 d.306 e.none of these

Answer: b.267

No of tails=2

This is a 2 tailed test

as we are checking the accuracy of plus minus 6%

sp=standard error of proportion=square root of (pq/n)

The maximum value of standard error of proportion for any given value of n is when p=q=0.5

confidence interval=95%

Z corresponding to 95%confidence interval and 2 tailed test is1.96

(from the tables or using EXCEL function NORMSINV)

We have to see that Z* sp < 6%

or sp < 6.%/Zor 6.% / 1.96

or sp < 0.030612=6%/1.96

But

sp=standard error of proportion=square root of (pq/n)

or n=(pq)/(sp^2)

The maximum value of standard error of proportion for any given value of n is when p=q=0.5

pq=0.25=0.5*0.5

or n=(pq)/(sp^2)=267=0.25/0.030612^2

Therefore sample size required for plus minus 6%accuracy is267

32) Samples of size 10 are selected from a normal population with a ...

#### Solution Summary

Anwers questions on Normal distribution, Binomial distribution, Probability, Confidence interval etc.

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.