AP Stats Normal Distribution Practice

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Scores on the ACT college entrance exam follow a Normal distribution with mean 21 and standard deviation 5. Wayne's standardized score on the ACT was -0.6. What was Wayne's actual ACT score?

• 3

• 13

• 16

• 18

• 24

An office uses two brands of fluorescent light bulbs in its overhead light fixtures. From past experience, it is known that Brand A bulbs have a mean life length of 3000 hours and a standard deviation of 200 hours, while Brand B bulbs have a mean life length of 2700 hours and a standard deviation of 250 hours. Which bulb has a longer life relative to all bulbs of its brand, a Brand A bulb that lasts 3150 hours or a Brand B bulb that lasts 2850 hours?

• The Brand A bulb has a longer life relative to its brand.

• The Brand B bulb has a longer life relative to its brand.

• The two bulbs have equally long lives.

Fuji apples grown at a certain orchard have a mean weight of 5.2 ounces with a standard deviation of 0.8 ounces. Suppose the scale the orchard owner uses systematically over weighs apples by 0.2 ounces and also weighs the apples in grams, rather than ounces. What would the mean and standard deviation of these apples’ weights be as determined by this scale? (Note: 1 ounce ≈ 28 grams).

• Mean 145.6 grams, standard deviation 22.4 grams.

• Mean 140 grams, standard deviation 22.4 grams.

• Mean 140 grams, standard deviation 16.8 grams.

In the class of 2016, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) follows an approximately Normal distribution with a mean of 508 and standard deviation of 110. About what 95% of students who took the SAT scored between _______ and _______?

• 398 and 618

• 288 and 728

• 398 and 728

• 288 and 618

A value found by subtracting the mean and dividing by the standard deviation is called _________________.

• standardized value

• statistic

• percentile

• Normal distribution

The heights of 5-year old boys are approximately normal. The mean height of a random sample of 37 5-year old boys is found to be 30 inches with a standard deviation of 3 inches. What is the standard error of x̄?

• .493

• 1.32

• 5.77

• 1.96

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 515 and standard deviation 114. You choose an SRS of 100 students and average their SAT Math scores. Suppose that you do this many, many times. Which of the following are the mean and standard deviation of the sampling distribution of x̄ ?

• Mean = 515; SD = 114

• Mean = 515; SD = 114/√100

• Mean = 515/100; SD = 114/√100

• Mean = 515/100; SD = 114/100

• Mean = 515/100; SD = 114/√100

2000 children were surveyed and the report that followed said, "With 98% confidence, between 20% and 50% of all parents make their children eat breakfast." What does 98% confidence mean in this situation?

• We can be 98% confident that the method used to get the intervals always gives the correct answer

• 98% of all parents will make their kids eat breakfast

• When used repeatedly, the method used to find the interval produces intervals which include the true proportion about 98% of the time

• The kids were 98% confident that they ate breakfast that day.

Mr. Reinecke wants to estimate the proportion of seniors who will go to college next year with 96% confidence and a margin of error of no more than 5%. What size sample does he need to take?

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