Question Help Use the normal distribution of SAT critical reading scores for which the mean is508and the standard deviation is110.Assume the variable x is normally distributed.(a)What percent of the SAT verbal scores are less than550?(b)If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than525?(a)Approximatelynothing%of the SAT verbal scores are less than550.(Round to two decimal places as needed.)(b)You would expect that approximatelynothingSAT verbal scores would be greater than525.(Round to the nearest whole number as needed.) 2)About76%of all female heart transplant patients will survive for at least 3 years.Seventyfemale heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than72%?Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal topqn.The probability that the sample proportion surviving for at least 3 years will be less than72%is(Round to four decimal places as needed.) 3)Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability. FindP(5)whenp=0.30.P(5)=nothing(Round to five decimal places as needed.) 4)Find the indicated area under the standard normal curve. Betweenz=−1.69andz=1.69 The area betweenz=−1.69andz=1.69under the standard normal curve is 5)A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of31,000miles and a standard deviation of2500miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Tires that wear out bymiles will be replaced free of charge.(Round to the nearest mile as needed.) 6)In the game of roulette, a player can place a$8bet on the number10and have a138probability of winning. If the metal ball lands on10,the player gets to keep the$8paid to play the game and the player is awarded an additional$280.Otherwise, the player is awarded nothing and the casino takes the player's$8.Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.The expected value is $ (Round to the nearest cent as needed.) 7)A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. A survey of adults found that59%have used a multivitamin in the past 12 months. You randomly select40adults and ask them if they have used a multivitamin in the past 12 months.Select the correct answer below and, if necessary, fill in the answer boxes within your choice. A.No, becausenp<5. B.No, becausenq<5. C.Yes, the mean isand the standard deviation is

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Use the normal distribution of SAT critical reading scores for which the mean is

508

and the standard deviation is

110.

Assume the variable x is normally distributed.

(a)	What percent of the SAT verbal scores are less than 550?
(b)	If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?

(a)

Approximately

nothing%

of the SAT verbal scores are less than

550.

(Round to two decimal places as needed.)

(b)

You would expect that approximately

nothing

SAT verbal scores would be greater than

525.

(Round to the nearest whole number as needed.)

About

76%

of all female heart transplant patients will survive for at least 3 years.

Seventy

female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than

72%?

Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to

pqn.

The probability that the sample proportion surviving for at least 3 years will be less than

72%

is
(Round to four decimal places as needed.)

Assume the geometric distribution applies. Use the given probability of success p to find the indicated probability.

Find

P(5)

when

p=0.30.

P(5)=nothing

(Round to five decimal places as needed.)

Find the indicated area under the standard normal curve.

Between

z=−1.69

and

z=1.69

The area between

z=−1.69

and

z=1.69

under the standard normal curve is

A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of

31,000

miles and a standard deviation of

2500

miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?

Tires that wear out by

miles will be replaced free of charge.

(Round to the nearest mile as needed.)

In the game of roulette, a player can place a

bet on the number

and have a

138

probability of winning. If the metal ball lands on

10,

the player gets to keep the

paid to play the game and the player is awarded an additional

$280.

Otherwise, the player is awarded nothing and the casino takes the player's

$8.

Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.

The expected value is $

(Round to the nearest cent as needed.)

A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.

A survey of adults found that

59%

have used a multivitamin in the past 12 months. You randomly select

adults and ask them if they have used a multivitamin in the past 12 months.

Select the correct answer below and, if necessary, fill in the answer boxes within your choice.

No, because

np<5.

No, because

nq<5.

Yes, the mean is

and the standard deviation is

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What percent of the SAT verbal scores are less than 550​? (b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525​?

What percent of the SAT verbal scores are less than 550? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?