he question was; what is the probability of rejecting the null hypothesis? Using the equation of the central limit theorem and the concepts of the normal distribution we made the following computation.

Therefore, the probability of rejection of the null hypothesis, as well as the likelihood of rejection and wrongly rejection is 5.74%.

Questions:

1. If you change the sample size to 36 samples, the probability of rejecting the null hypothesis and committing type I error is higher?

1. True
2. False

2. If you change the sample size to 4 samples, the probability of rejecting the null hypothesis and committing type I error is higher?

1. True
2. False

3. Why do you think that the size is important in hypothesis testing? Answer in your own words.

An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74 inch. The lower and upper specification limits under which the ball bearings can operate are 0.72 inch and 0.76 ​inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.743 inch and a standard deviation of 0.005 inch.

A. What is the probability that a ball bearing is between the target and the actual​ mean?

B. What is the probability that a ball bearing is between the lower specification limit and the target?

C. What is the probability that a ball bearing is above the upper specification limit?

D. What is the probability that a ball bearing is below the lower specification limit?

There are two types of potential borrowers in equal numbers among the population. All haveprojects that require an investment of $100, which must be borrowed. Type A projects yield agross return of $130 in one year with probability .8; they fail and yield 0 with probability .2. Type B projects yield a gross rate of return of $250 with probability.4, but fail, yielding zero,with probability .6.Potential lenders require an expected gross return of $102 on $100 loaned. With symmetricinformation, who will get financing and why? Now suppose the project expected returns areprivate information. Lenders cannot distinguish one type from another. Will any lending occur?Why or why not? Explain in detail.

Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose thatP(A) = 0.7and P(B) = 0.3.

(a)Could it be the case thatP(A ∩ B) = 0.5?

Why or why not?

(b) From now on, suppose thatP(A ∩ B) = 0.2.

What is the probability that the selected student has at least one of these two types of cards?

(c)What is the probability that the selected student has neither type of card?

(d)Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.

Calculate the probability of this event.

(e) Calculate the probability that the selected student has exactly one of the two types of cards.

Assume that females have pulse rates that are normally distributed with a mean of

mu equals 76.0μ=76.0

beats per minute and a standard deviation of

sigma equals 12.5σ=12.5

beats per minute. Complete parts​ (a) through​ (c) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between

7272

beats per minute and

8080

beats per minute.The probability is

nothing.

​(Round to four decimal places as​ needed.)

b. If

2525

adult females are randomly​ selected, find the probability that they have pulse rates with a mean between

7272

beats per minute and

8080

beats per minute.The probability is

nothing.

​(Round to four decimal places as​ needed.)

The length of human pregnancies is approximately normal distributed with mean =266 days and Standard Deviation = 16 days ( 20 points ) . Exercise 8.1 What is the probability a randomly selected pregnancy lasts less than 260 days? Suppose a random sample of 20 pregnancies is obtained. Describe the sample distribution the sampling distribution of sample mean of human pregnancies. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less? What is probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less? What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

A courier service company has found that their delivery time of parcels to clients is approximately normally distributed with a mean delivery time of 50 minutes and a variance of 25 minutes (squared).

a) What is the probability that a randomly selected parcel will take 60 minutes to deliver? [2]

b) What is the probability that a randomly selected parcel will take between 38.75 and 55 minutes to deliver? [5]

c) What is the probability that a randomly selected parcel will take more than 36.25 minutes to deliver? [3]

d) What is the probability that a randomly selected parcel will take more than 59.25 minutes to deliver? [3]

e) What is the minimum delivery time for the 2.5% of parcels with the longest time to deliver?   

83. Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.

a. Define the random variable. X= ________________.

b. Is X continuous or discrete?

c. μ= ________

d. σ= ________

e. Draw a graph of the probability distribution. Label the axes.

f. Find the probability that a phone call lasts less than nine minutes.

g. Find the probability that a phone call lasts more than nine minutes.

h. Find the probability that a phone call lasts between seven and nine minutes.

i. If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?

The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose we have an iid sample of size 100 of these components

Some hints: P(X < c) for an exponential(lambda) can be found via pexp(c,lambda) E[X] = 1/lambda and Var[X] = 1/lambda^2

Round all answers to 4 decimals

Using the exact probability distribution, what is the probability that a single component will be within 15.38 units of the population mean?

Using Chebyshev's inequality, what is a lower bound on the probability that the sample mean will be within 15.38 units of the population mean?

Using the CLT, what is an approximation to the probability that the sample mean will be within 15.38 units of the population mean?