6.3 Estimating the Binomial with the Normal Distribution — Introductory Business Statistics 2e

6.3 Exercise 2

Let’s assume that only 10% of the wooden furniture made by a carpenter is made to the exact dimensions in the blueprint. During the last 3 years, the carpenter has made 100 pieces of wooden furniture, and 16 were found to be made to the exact dimensions in the blueprint.

What is the probability that, in 100 wooden furniture items, more than 16 would be made to the exact dimensions of the blueprint…

2.5

6.3 Exercise 5

Is P(x < 1) equal to P(x ≤ 1)? Why?

2.5

6.3 Exercise 9

If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x?

2.5

6.3 Exercise 11

X ~ N(54, 8)

Find the probability that x < 30.

2.5

6.3 Exercise 13

X ~ N(54, 8)

X ~ N(–3, 4)

Find the probability that x is between one and four.

2.5

6.3 Exercise 17

X ~ N(54, 8)

An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have at least 45 successes.

2.5

6.3 Exercise 18

X ~ N(54, 8)

An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have at least 22 successes.

2.5

6.3 Exercise 19

X ~ N(54, 8)

An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have from 35 to 45 successes.

2.5

6.3 Exercise 20

X ~ N(54, 8)

An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have from 26 to 30 successes.

2.5

6.3 Exercise 21

X ~ N(54, 8)

An experiment with a probability of success given as 0.40 is repeated 100 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have at most 34 successes.

2.5

6.3 Exercise 22

X ~ N(54, 8)

An experiment with a probability of success given as 0.30 is repeated 90 times. Use the normal distribution to approximate the binomial distribution, and find the probability the experiment will have at most 34 successes.

2.5

6.3 Exercise 23

X ~ N(54, 8)

A multiple choice test has a probability any question will be guesses correctly of 0.25. There are 100 questions, and a student guesses at all of them. Use the normal distribution to approximate the binomial distribution, and determine the probability at least 30, but no more than 32, questions will be guessed correctly.

2.5

6.3 Exercise 24

X ~ N(54, 8)

A multiple choice test has a probability any question will be guesses correctly of 0.25. There are 100 questions, and a student guesses at all of them. Use the normal distribution to approximate the binomial distribution, and determine the probability at least 24, but no more than 28, questions will be guessed correctly.

2.5