Regular gasoline averaged ​$2.83 per gallon in December 2018. Assume the standard deviation for gasoline prices is ​$0.14 per gallon. A random sample of 40 service stations was selected. Complete parts a through d.

a. What is the probability that the sample mean will be less than ​$2.84?

The probability that the sample mean will be less than $2.84 is ______

​(Type an integer or decimal rounded to four decimal places as​ needed.)

b. What is the probability that the sample mean will be more than ​$2.87?

The probability that the sample mean will be more than ​$2.87 is ________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

c. What is the probability that the sample mean will be between $2.81 and $2.91​?

The probability that the sample mean will be between $2.81 and ​$2.91 is _________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

d. Suppose the sample mean is $2.89. Does this result support the average gasoline price​ findings? Explain your answer.

The probability that the average price per gallon is more than ​$2.89 is ________.

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Does this result support the average gasoline price findings? Explain your answer. Consider a probability of less than 0.05 to be small.

A) The probability supports the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is small.

B) The probability does not support the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is large. "

C)The probability supports the finding that the average price per gallon for gas in the population is ​$2.83, because this probability is large.

D)The probability does not support the finding that the average price per gallon for gas in the population is ​$2.83​, because this probability is small.

A new technology for the production of liquid-crystal displays (LCD) is being mastered. 8,000,000 pixels are located on the LCD. The LCD is defective if there are more than 5 malfunctioning pixels. Let denote the number of defective pixels observed on the LCD. Of 3,000 LCD inspected, the following data were observed for the values of :

Does the assumption of the Poisson distribution seem appropriate as a probability model for these data? Use α=0.9.

1. If the percent recombination between A and B is 12, Between A and C 4, and between B and C is 8 then the order of the genes on the chromosome is?

2. A man who is homozygous for type A blood has a child with a woman who is homozygous for type B blood. What is the probability that this child will have type AB blood?

3. In familial hypercholesterolemia, individuals homozygous for the allele causing the disorder completely lack receptors on liver cells that take up cholesterol from the bloodstream. Heterozygotes have one-half the number of receptors while individuals homozygous for the normal allele are phenotypically normal. This is an example of _____.

44​% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four. ​(a) ​P(5)equals nothing ​(Round to three decimal places as​ needed.) ​(b) ​P(xgreater than or equals​6)equals nothing ​(Round to three decimal places as​ needed.) ​(c) ​P(xless than​4)equals nothing ​(Round to three decimal places as​ needed.)

Approximately 300 million golf balls were lost in the U.S. in 2009. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson random variable with a mean of 3 balls. What is the probability that:

0 balls will be lost in an 18-hole round?

An individual can play an 18-hole round with a single sleeve of golf balls (3 balls)? (Hint: can you continue to play if you have lost all 3 balls?)

An individual who is going to play 3 rounds of golf on a trip can play all three rounds with the single sleeve of balls?

In exercise 6, determine whether you can use a normal distribution t approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities.

1. A survey of U.S. adults found that 64% watch NFL football. You randomly select 20 U.S. adults and ask them whether they watch NFL football. Find the probability that the number who watch NFL football is:

1. Exactly 10
2. Less than 7
3. At least 15
4. Identify any unusual events

Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one, with the biased die made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities.

(i) P(6 is rolled)

(ii) P(biased die used — 6 is rolled)

(iii) P(biased die used — 6 not rolled)

(iv) The number of 6's in a row we would need to see before it is more likely that we had been using the biased die

A local Division of Motor Vehicles (DMV) is concerned with its waiting line system. Currently, the DMV uses a single-server, single-line, single-phase system when processing license renewals. Based on historical evidence, the average number of customers arriving per hour is 9 and is described by a Poisson distribution. The service rate is 12 customers per hour with the service times following an exponential distribution. The customers are patient and come from an infinite population. The manager of the DMV would like you to calculate the operational characteristics of the waiting line

What is the probability that there are 2 customers in the system.
​ ​ ​ ​ ​ ​ ​

A random sample of 15 people was asked to record how much TV they watched every day for a week. The total number of hours each person watched during the week is displayed below.

a. Is a normal approximation appropriate here?

A. Yes
B. No

The data are shown below.

b. If a normal approximation is appropriate, find the probability that a randomly selected person in the population watches less than 9 of TV per week. If a normal approximation is not appropriate, type “NA” (without the quotes).

You have four hard drives. Two of the drives have a failure rate of 1.75% (pf = 0.0175), and the other two have a failure rate of 2.5%. Assume that failures of the hard drives are independent events. (a) What is the probability of failure of your system? (b) Assuming that your quantities of 1.75% and 2.5% drives remain equal (that is, you have n 1.75% and n 2.5% drives), what is the minimum total number of hard drives your system would have to have to exceed a 50% failure rate?

(Note: failure of the system is defined to be the failure of one of the hard drives.)