Assignment No. 2
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Question 1
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A survey report states that 70% of adult women visit their doctors for
physical examination at least once in two years. If 19 adult women are
randomly selected, find the probability that

(a) fewer than 14 of them have had a physical examination in the past
    two years;

(b) at least 17 of them have had a physical examination in the past
    two years.

Compute the required probabilities exactly (i.e., use statistical
tables) and approximately (i.e., use normal approximations) and compare
your results.


Question 2
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The strength of cardboard mailing tubes (as measured by the force
required to puncture them with a sharp object) is normally distributed
with mean 32 lbs and standard deviation 4 lbs.

(a) What is the probability that a tube will puncture if it is struct by
    a 25 lb blow with the object?

(b) Find the 99-th percentile of the given normal distribution and
    interpret your result.


Question 3
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In a study of the nutritional qualities of fast foods, the amount of fat
was measured for a random sample of 25 hamburgers of a particular
restaurant chain. The mean and standard deviation were found to be 30.2
and 3.8 grams, respectively. Past experience suggests that fat content
in hamburgers follow a normal distribution.

(a) Use the given summary statistics to construct a 95% confidence
    interval for the average fat content in hamburgers served in these
    restaurants.

(b) Suppose you are now told that it is known that the variance for the
    amount of fat in a hamburger is 16 gm^2. How does this affect your
    calculation of the required confidence interval?


Question 4
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A medical researcher conjectures that smoking can result in wrinkled
skin around the eyes. By observing 150 smokers and 250 nonsmokers, the
researcher finds that 95 of the smokers and 103 of the nonsmokers have
prominent wrinkles around their eyes.

(a) Suggest an appropriate estimand for this problem and obtain
    a 90% confidence interval for it.

(b) Do these data substantiate the belief that prominent wrinkles around
    the eyes are more prevalent among smokers than nonsmokers?

(c) If the results are statistically significant, can the researcher
    readily conclude that smoking causes wrinkles around the eyes? Why
    or why not?