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Chapter 7: Q. 56 (page 479)
Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of to be ? Justify your answer.
If the sample's standard deviation of the sampling distribution is , the sample should be 16 axles.
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The mean of this distribution (don’t try to find it) will be
a. very close to the median.
b. greater than the median.
c. less than the median.
d. You can’t say, because the distribution isn’t symmetric.
e. You can’t say, because the distribution isn’t Normal.
Birth weights Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weights is approximately Normal with a mean of 3668 grams and a standard deviation of 511 grams.
a. Sketch a graph that displays the distribution of birth weights for this population.
b. Sketch a possible graph of the distribution of birth weights for an SRS of size $5 . Calculate the range for this sample.
In this population, the range (Maximum - Minimum) of birth weights is 3417 grams. We technology to take 500 SRSs of size and calculate the range (Maximum Minimum) for each sample. The dotplot shows the results.
Healthy Living From a large group of people who signed a card saying they intended to quit smoking, people were selected at random. It turned out that of these individuals had not smoked over the past months.
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.
A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.
a. Without doing any calculations, explain which event is more likely:
b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).
c. Calculate the probability of the second event in part (a).
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