Sketch a normal curve with the following parameters. (For part (a) through part (d), select the correct graph.)

(a)

mean of 15 and standard deviation of 2

(b)

mean of 15 and standard deviation of 3

(c)

mean of 12 and standard deviation of 2

(d)

mean of 12 and standard deviation of 3

(e)

Consider two normal curves. If the first one has a larger mean than the second one, must it have a larger standard deviation as well? Explain your answer. No. The values of and are independent. Yes. As increases, must also increase.No. As increases, will decrease. Yes. The values of and are independent.

0

What percentage of the area under the normal curve lies as given below?

(a)

to the right of (Enter an exact number.)

1 %

(b)

between 2 and + 2 (Enter an exact number.)

2 %

(c)

to the right of + 3 (Enter a number. Use 2 decimal places.)

3 %

0

What are the values of the mean and standard deviation of a standard normal distribution? (For each answer, enter an exact number.)

= 1

= 2

0

• A normal distribution has = 28 and = 5.

(a)

Find the z score corresponding to x = 23. (Enter an exact number.)

1

(b)

Find the z score corresponding to x = 42. (Enter a number.)

2

(c)

Find the raw score corresponding to z = 3. (Enter an exact number.)

3

(d)

Find the raw score corresponding to z = 1.3. (Enter a number.)

4

0

Raul received a score of 79 on a history test for which the class mean was 70 with a standard deviation of 9. He received a score of 70 on a biology test for which the class mean was 70 with standard deviation 8. On which test did he do better relative to the rest of the class?

biology test history testthe same

0

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean = 25.7 kilograms and standard deviation = 3.4 kilograms. Let x be the weight of a fawn in kilograms. For parts (a), (b), and (c), convert the x intervals to z intervals. (For each answer, enter a number. Round your answers to two decimal places.)

(a)

x < 30

z < 1

(b)

19 < x (Fill in the blank. A blank is represented by _____.)

_____ < z

2

(c)

32 < x < 35 (Fill in the blanks. A blank is represented by _____. There are two answer blanks.)

_____ < z < _____

For parts (d), (e), and (f), convert the z intervals to x intervals. (For each answer, enter a number. Round your answers to one decimal place.)

(d)

2.17 < z (Fill in the blank. A blank is represented by _____.)

_____ < x

5

(e)

z < 1.28

x < 6

(f)

1.99 < z < 1.44 (Fill in the blanks. A blank is represented by _____. There are two answer blanks.)

_____ < x < _____

(g)

If a fawn weighs 14 kilograms, would you say it is an unusually small animal? Explain using z values and the figure above. Yes. This weight is 3.44 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. Yes. This weight is 1.72 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.No. This weight is 3.44 standard deviations below the mean; 14 kg is a normal weight for a fawn. No. This weight is 3.44 standard deviations above the mean; 14 kg is an unusually high weight for a fawn. No. This weight is 1.72 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.

(h)

If a fawn is unusually large, would you say that the z value for the weight of the fawn will be close to 0, 2, or 3? Explain. It would have a z of 0. It would have a negative z, such as 2.It would have a large positive z, such as 3.

0

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

= 6; = 2

P(5 x 8) = 1

0

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

= 26; = 4.2

P(x 30) = 1

0

Find z such that 88.1% of the standard normal curve lies to the left of z. (Enter a number. Round your answer to two decimal places.)

z = 1

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

0

Find z such that 6% of the standard normal curve lies to the right of z. (Enter a number. Round your answer to two decimal places.)

z = 1

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

0

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 of 6.0 minutes and a standard deviation of 1.5 minutes. 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 between 3 and 7 minutes

1

(b)

the response time is less than 3 minutes

2

(c)

the response time is more than 7 minutes

3

0

Suppose x has a distribution with a mean of 60 and a standard deviation of 45. Random samples of size n = 36 are drawn.

(a)

Describe the distribution.

has a geometric distribution. has a binomial distribution. has an approximately normal distribution. has an unknown distribution. has a normal distribution. has a Poisson distribution.

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

= mu sub x bar = 2

= sigma sub x bar =3

(b)

Find the z value corresponding to = 75. (Enter an exact number.)

z = 4

(c)

Find P( < 75). (Enter a number. Round your answer to four decimal places.)

P( < 75) = P(x bar < 75)5

(d)

Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 75? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 75. Yes, it would be unusual because less than 5% of all such samples have means less than 75.Yes, it would be unusual because more than 5% of all such samples have means less than 75. No, it would not be unusual because less than 5% of all such samples have means less than 75.

0

Consider an x distribution with standard deviation = 18. (For each answer, enter an exact number.)

(a)

If specifications for a research project require the standard error of the corresponding distribution to be 2, how large does the sample size need to be?

n = 1

(b)

If specifications for a research project require the standard error of the corresponding distribution to be 1, how large does the sample size need to be?

n = 2

0

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19.

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

(a)

Suppose n = 31 and p = 0.28. (For each answer, enter a number. Use 2 decimal places.)

np = 1

nq = 2

Can we approximate p by 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 _____ _____.

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

_p = mu sub p hat = 7

_p = sigma sub p hat = 8

(b)

Suppose n = 25 and p = 0.15. Can we safely approximate p by 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 _____ _____.

(c)

Suppose n = 49 and p = 0.18. (For each answer, enter a number. Use 2 decimal places.)

np = 13

nq = 14

Can we approximate p by 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

nq exceeds np exceedsboth np and nq exceed nq does not exceed np does not exceed np and nq do not exceed

fourth blank (Enter an exact number.)

18

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

_p = mu sub p hat = 19

_p = sigma sub p hat = 20