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determine the area of the region indicated 1.32<z<2.47


Consider the normal distribution of IQs with a mean of 100 and a standard deviation of 16. What percentage of IQs are

a. greater than 95?

b. less than 120

c. between 90 and 110

 



What's More



Let's see how well you understood our discussion. At this point, I want you to



solve the following problems. Show your complete solution by following the step-by-



step procedure.



1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand



of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is



normally distributed.



a. If a cup of ice cream is selected, what is the probability that the cholesterol



content will be more than 670 mg?



b. If a sample of 10 cups of ice cream is selected, what is the probability that



the mean of the sample will be larger than 670 mg?



2. In a study of the life expectancy of 400 people in a certain geographic region, the



mean age at death was 70 years, and the standard deviation was 5.1 years. If a



sample of 50 people from this region is selected, what is the probability that the



mean life expectancy will be less than 68 years?




Tests made on the breaking strength of 10 pieces of a metal gave the following results: 578, 572, 570, 568, 572, 570, 570, 572, 598 and 584 kg. Test if the mean breaking strength of the wire can be assumed as 577 kg.

"An electrical firm produces light bulbs that have a length of life that is approximately normally distributed with a mean of 870 hours and a population standard deviation of 27 hours. A new version of light bulbs is being produced and is assumed to be better than the previous version. To test this claim, a random sample of 59 new light bulbs are tested. Would you buy the new version of the light bulb or would you buy the older version if the random sample showed an average of 720 hours? Use a 0.05 level of significance."


a. I will buy the new version.

b. I will certainly buy the older version because I am 100% sure it is better.

c. There is no sufficient data to make a sound conclusion.

d. I will buy the older version until there is sufficient evidence to do otherwise.


"It is claimed that a car is driven on the average less than 23100 kilometers per year with a population standard deviation of 2100 kilometers. A company wants to test if their current car model is on par with this average. To test this, a random sample of 70 cars from the company were tested. Suppose you are an analyst of the company, would you suggest to make improvements in your car design if the random sample showed an average of 22100 kilometers? Use a 0.1 level of significance."


a. There is no sufficient data to make a sound conclusion.

b. I would recommend an improvement to the car design to improve performance.

c. I will assume that the cars are on par with the average and recommend to do nothing.

d. I will be certain that there is no need to improve the car design based on the result.



"An electrical firm produces light bulbs that have a length of life that is approximately normally distributed with a mean of 680 hours and a population standard deviation of 26 hours. A new version of light bulbs is being produced and is assumed to be better than the previous version. To test this claim, a random sample of 93 new light bulbs are tested. Would you agree with this claim if the random sample showed an average of 920 hours? Use a 0.1 level of significance.


What are the given? Write only the number. :

population mean: Blank 1 hours

population standard deviation: Blank 2 hours

sample size: Blank 3

sample mean: Blank 4 hours

level of significance: Blank 5


What is the critical value?

z: Blank 6


What is the value of the calculated z? Round your answer to the nearest hundredths.

z: Blank 7"


"It is claimed that a car is driven on the average less than 24700 kilometers per year with a population standard deviation of 2900 kilometers. To test this claim, a random sample of 55 car owners are asked to keep a record of the kilometers they travelled. Would you agree with this claim if the random sample showed an average of 20100 kilometers? Use a 0.05 level of significance.


What are the given? Write only the number. :

population mean: Blank 1 km

population standard deviation: Blank 2 km

sample size: Blank 3

sample mean: Blank 4 km

level of significance: Blank 5


What is the critical value?

z: Blank 6


What is the value of the calculated z? Round your answer to the nearest hundredths.

z: Blank 7"


The average height of students in a freshman class of a certain school has been 153.24 cm with a population standard deviation of 4.03 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 41 students in the present freshman class has an average height of 170.16 cm? Use a 0.05 level of significance.


What are the given? Write only the number. :

population mean: Blank 1 cm

population standard deviation: Blank 2 cm

sample size: Blank 3

sample mean: Blank 4 cm

level of significance: Blank 5


What are the critical values? Write the positive critical value first then the negative.

z: Blank 6 and Blank 7


What is the value of the calculated z? Round your answer to the nearest hundredths.

z: Blank 8


Sample Mean (x

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(x¯)FrequencyProbability P(x

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