Letzbe a random variable with a standard normal distribution. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

P(z1.41) =

Shade the corresponding area under the standard normal curve. (Select the correct graph.)

12.

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BBBasicStat8Acc 7.3.005.MI.

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Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

=8;=2

P(7x11) =

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Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

=28;=4.4

P(x30) =

14.

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BBBasicStat8Acc 7.3.018.MI.

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Findzsuch that88.3%of the standard normal curve lies to the left ofz. (Enter a number. Round your answer to two decimal places.)

z=

Sketch the area described. (Select the correct graph.)

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BBBasicStat8Acc 7.3.019.MI.

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Findzsuch that8%of the standard normal curve lies to the right ofz. (Enter a number. Round your answer to two decimal places.)

z=

Sketch the area described. (Select the correct graph.)

16.

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BBBasicStat8Acc 7.3.028.MI.

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Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of8.4minutesand a standard deviation of1.7minutes.For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)

(a)

the response time is between5and10minutes

(b)

the response time is less than5minutes

(c)

the response time is more than10minutes

17.

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BBBasicStat8Acc 7.5.006.MI.

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Supposexhas a distribution with a mean of80and a standard deviation of3. Random samples of sizen=36are drawn.

(a)Describe thedistribution.

has a geometric distribution.

has a Poisson distribution.

has a normal distribution.

has an approximately normal distribution.

has a binomial distribution.

has an unknown distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

=

mu sub x bar =

=

sigma sub x bar =

(b)Find thezvalue corresponding to=79. (Enter an exact number.)

z=

(c)FindP(<79). (Enter a number. Round your answer to four decimal places.)

P(<79) =

P(x bar < 79)

(d)Would it be unusual for a random sample of size36from thexdistribution to have a sample mean less than79? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 79.

Yes, it would be unusual because less than 5% of all such samples have means less than 79.

Yes, it would be unusual because more than 5% of all such samples have means less than 79.

No, it would not be unusual because less than 5% of all such samples have means less than 79.

18.

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BBBasicStat8Acc 7.5.010.MI.

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Consider anxdistributionwith standard deviation=22. (For each answer, enter an exact number.)

(a)If specifications for a research project require the standard error of the correspondingdistributionto be2, how large does the sample size need to be?

n=

(b)If specifications for a research project require the standard error of the correspondingdistributionto be 1, how large does the sample size need to be?

n=

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Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a)Supposen=36andp=0.32.(For each answer, enter a number. Use 2 decimal places.)

np=

nq=

Can we approximatepby a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____,p_____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

npandnqdo not exceed

bothnpandnqexceed

npdoes not exceed

nqexceeds

nqdoes not exceed

npexceeds

fourth blank (Enter an exact number.)

What are the values of_pand_p? (For each answer, enter a number. Use 3 decimal places.)

_p=

mu sub p hat =

_p=

sigma sub p hat =

(b)Supposen= 25 andp= 0.15.Can we safely approximatepby a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____,p_____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

npandnqdo not exceed

bothnpandnqexceed

npdoes not exceed

nqexceeds

nqdoes not exceed

npexceeds

fourth blank (Enter an exact number.)

(c)Supposen=40andp=0.30.(For each answer, enter a number. Use 2 decimal places.)

np=

nq=

Can we approximatepby a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____,p_____ be approximated by a normal random variable because _____ _____.

first blank

Yes

No

second blank

can

cannot

third blank

npandnqdo not exceed

bothnpandnqexceed

npdoes not exceed

nqexceeds

nqdoes not exceed

npexceeds

fourth blank (Enter an exact number.)

What are the values of_pand_p? (For each answer, enter a number. Use 3 decimal places.)

_p=

mu sub p hat =

_p=

sigma sub p hat =