Question

1. Find the area under the standard normal curve (round to four decimal places)

a. To the left of z=1.65

b. To the right of z = 0.54

c. Between z = -2.05 and z = 1.05

2. Find the z-score that has an area of 0.23 to its right.

3. The average height of a certain group of children is 49 inches with a standard deviation of 3 inches. If the heights are normally distributed, find the probability that a randomly selected child’s height will be: (note: round to four decimal places)

a. Less than 45 inches.

b. Between 50 and 55 inches.

4. Scores on a statistics were normally distributed with a mean of 72 and a standard deviation of 9. Find the 80th percentile of the scores.

5. A population has mean m = 184 and s = 33 . Find m x and s x for samples of size n = 64 . (round s x to three decimal places).

6. A sample of size 25 will be drawn from a skewed population with mean 60 and standard deviation 7. Is it appropriate to use the normal distribution to find probabilities for x ? Explain your answer.

7. Among all the state income tax forms filed in a particular state, the mean income tax paid was m = $1950 and the standard deviation was s = $490 . As part of a study of the impact of a new tax law, a sample of 100 income tax returns is examined. What is the probability that the sample mean of these 100 returns is greater than $2050? Would this be unusual? Round your probability to four decimal places.

8. A sample of size n = 137 is drawn from a population with a proportion p = 0.16 . Let ˆp be the sample proportion.

a. What specific conditions must be met in order to use the standard normal distribution to find probabilities for ˆp?

b. Find m ˆp and s ˆp . Round s ˆp to four decimal places.

c. Find P(ˆp < .13). Round to four decimal places.

9. The amount of time that a certain cell phone will keep a charge is known to be normally distributed with a standard deviation s = 15 hours. A sample of 45 cell phones has a mean time of 145 hours. Let m represent the population mean time that

a cell phone will keep a charge.

a. What is the point estimate of m ?

b. What is the standard error of the point estimate? Round to three decimal places.

c. Suppose that a 90% confidence interval is to be constructed for the mean time. Find the margin of error for this confidence interval (use three decimal places).

e. Construct the 90% confidence interval and interpret your result:

f. What sample size would be necessary so that a 98% confidence interval will have a margin of error of 2 hours?

10. Circle the correct word: If we decrease the sample size and keep the confidence level the same, we increase / decrease the margin of error.

11. Use Table A.3 to find the critical value ta /2 needed to construct a confidence interval of the given level with the given sample size:

a. Level 99%, sample size 19

b. Level 90%, sample size 172

12. In a sample of 133 hip surgeries of a certain type, the average surgery time was 130.2 minutes with a standard deviation of 24.6 minutes. Construct a 90% confidence interval for the mean surgery time for this procedure and interpret your result. Round your answer to one decimal place.

13. Scores on a standardized reading test in a certain school district have a mean of 75. After modifications to the reading curriculum were made, an educator believes that the mean may now higher. State the appropriate null and alternate hypotheses.

14. It is desired to check the calibration of a scale by weighing a standard 10-gram weight 100 times. Let m be the population mean reading on the scale, so that the scale is in calibration if m=10 and out of calibration if m¹10. A test is made of the hypotheses H 0 : m = 10 versus H 1 : m ¹ 10 . Consider three possible conclusions: (i) The scale is in calibration. (ii) The scale is not in calibration. (iii) The scale might be in calibration.

a) Which of these three conclusions is best if H0 is rejected?

b) Assume that the scale is in calibration, but the conclusion is reached that the scale is not in calibration. Which type of error is this?

15. A test is made of H0 :m=40 versus H1:m>40. A sample of size n=75 is drawn, and x = 45 . The population standard deviation is s = 16 .

a. Compute the value of the test statistic z .

b. Is H 0 rejected at the a = 0.05 level?

16. For the following MINITAB output:

a. What are the null and alternate hypotheses?

b. What is the P-value?

c. Using the P-value approach, do you reject H 0 at the a = 0.05 level? State a conclusion.

17. For the past several years, the mean number of people in a household has been declining. A social scientist believes that in a certain large city, the mean number of people per household is less than 2.5. To investigate this, she takes a simple random sample of 250 households in the city, and finds that the sample mean number of people is 2.3 with a sample standard deviation of 1.3. Can you conclude that the mean number of people per household is less than 2.5?

a. State the null and alternate hypotheses.

b. Should we perform a z-test or a t-test? c. Compute the value of the test statistic.

d. Do you reject H0 at the a = 0.01 level?

e. State a conclusion.

Answer #1

For the standard normal distribution, compute Z0.69.
Use Excel and round the answer to two decimal places.
Consider the following test performed with the level of
significance 0.01: A random sample of size 28 is obtained from a
normally distributed population. The population standard deviation
is equal to 3.6. The sample mean happened to be 24. For this
hypothesis test, what will be the critical value (the relevant
z-alpha)? Round the answer to three decimal
places.
A probability distribution of all...

a.) For a standard normal curve, find the area between z = 0.28
and z = 1.95. (Use 4 decimal places.)
b.) Find the positive z value such that 89% of the
standard normal curve lies between –z and z. (Use
2 decimal places.)
c.) Given a normal distribution with population standard
deviation of 21 and a mean of μ = 29. If a random sample
of size 62 is drawn, find P(29 ≤ x ≤ 31).
Round to three...

Compute the area under the standard normal curve. Round your
answers to four decimal places. (a) The area to the right of z =
1.81 equals
(b) The area to the left of z = − 1.5 equals
(c) The area between z = 0 and z = 3.33 equals
PLEASE SHOW WORK

A sample of 25 observations is selected from a normal population
where the population standard deviation is 32. The sample mean is
77.
a.
Determine the standard error of the mean. (Round the final
answer to 3 decimal places.)
The standard error of
the mean is .
b.
Determine the 95% confidence interval for the population mean.
(Round the z-value to 2 decimal places. Round the
final answers to 3 decimal places.)
The 95% confidence
interval for the population mean...

A sample of 29 observations is selected from a normal population
where the population standard deviation is 40. The sample mean is
89.
a. Determine the standard error of the mean.
(Round the final answer to 3 decimal places.)
The standard error of the mean is .
b. Determine the 98% confidence interval for
the population mean. (Round the z-value to 2
decimal places. Round the final answers to 3 decimal
places.)
The 98% confidence interval for the population mean is...

1- Find the area under the standard normal curve between z=0.76
and z=1.90.
Round your answer to four decimal places.
2- Find the area under the standard normal curve between z=-2.49
and z=-0.44.
Round your answer to four decimal places.
3- Find the area under the standard normal curve between z=-2.26
and z=1.88.
Round your answer to four decimal places.
4- Find the area under the standard normal curve to the right of
z=2.37.
Round your answer to four decimal...

1. For a standard normal distribution,
find:
P(z > 2.32)
Keep four decimal places.
2. For a standard normal distribution,
find:
P(-0.9 < z < 0.95)
3. For a standard normal distribution,
given:
P(z < c) = 0.7622
Find c.
4. For a standard normal distribution,
find:
P(z > c) = 0.1753
Find c
5. Assume
that the readings at freezing on a batch of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C....

1. A sample size of n = 70 is drawn from a population with
proportion p = 0.32. Let p̂ be the sample proportion.
Find p̂m and p̂s . Round the standard deviation to four decimal
places.
Find )28.0p̂P ( > .
Find )40.0p̂P ( <
2. On a certain television channel, 20% of the
commercials are local advertisers. A sample of 150 commercials is
selected. Would it be unusual for more than 26% of the commercials
to be local advertisers?...

A) About _____% of the area under the curve of the standard
normal distribution is outside the interval
z=[−2.08,2.08]z=[-2.08,2.08] (or beyond 2.08 standard deviations of
the mean).
B) Assume that the readings at freezing on a batch of
thermometers are normally distributed with a mean of 0°C and a
standard deviation of 1.00°C. A single thermometer is randomly
selected and tested. Find the probability of obtaining a reading
less than -0.491°C.
P(Z<−0.491)=P(Z<-0.491)=
C) In a recent year, the Better Business...

1.Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.)The area to the left of
z = −1.44 is ____________
2 Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.)The area to the right of z = 1.62
is___.
3.Sketch the area under the standard normal curve over the
indicated interval...

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