<h1>Over the Winter Break, we had a 100 question worksheet and I’ve did all of them except six of them. I would appreciate it if someone helps me on these problems.</h1>
<li><p>The Gallup Poll asked a probability sample of 1785 adults whether they attended church or synagogue during the past week. Suppose that 40% of the adult population did attend. We would like to know the probability that an SS of sixe 1785 would come within plus or minus 3 percentage points of this true value.
a)If p-hat is the proportion of the sample who did attend church or synagogue, what is the mean of the sampling distribution of p-hat? What is its standard deviation?
b) Explain why you can use the normal approximation for the standard deviation of p-hat in this setting (rule of thumb 1).
c)Check that you can use the normal approximation for the distribution of p-hat (rule of thumb 2).
d) Find the probability that p-hat takes a value between 0.37 and 0.43. Will an SRS of size 1785 usually give a result p-hat within plus or minus 3 percentage points of the true population proportion? Explain.</p></li>
<li><p>According to a market research firm, 52% of all residential telephone numbers in Los Angeles are unlisted. A telephone sales firm uses random digit dialing equipment that dials residential numbers at random, whether or not they are listed in the telephone directory. The firm calls 500 numbers in Los Angeles.
a) What are the mean and standard deviation of the proportion of unlisted numbers in the sample?
b) What is the probability that at least half the numbers dialed are unlisted? (Remember to check that you can use the normal approximation.)</p></li>
<li><p>A study of the health of teenagers plans to measure the blood cholesterol level of an SRS of youth of ages 13 to 16 years. The researchers will report the mean x-bar from their sample as an estimate of the mean cholesterol level μ (mu) in this population.
a) Explain to someone who knows no statistics what it means to say that x-bar is an “unbiased” estimator of μ (mu).
b)The sample result x-bar is an unbiased estimator of the population parameter μ (mu) no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large sample gives more trustworthy results than a small sample.</p></li>
<li><p>An automatic grinding machine in an auto parts plant prepares axles with a target diameter (mu) μ=40.125 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is (sigma) σ=0.002 mm. The machine operator inspects a sample of 4 axles each hour for quality control purposes and records the sample mean diameter.
a) What will be the mean and standard deviation of the numbers recorded? Do your results depend on whether or not the axle diameters have a normal distribution?
b) Can you find the probability that an SRS of 4 axles has a mean diameter greater than 40.127 mm? If so, do it. If not, explain why not.</p></li>
<li><p>A study of rush-hour traffic in Sasn Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.5 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hours.
a) Could the exact distribution of the count be normal? Why or why not?
b) Traffic engineers estimate that the capacity of the interchange is 700 cars per hour. According to the central limit theorem, what is the approximate distribution of the mean number of persons x-bar in 700 randomly selected cars at this interchange?
c) What is the probability that 700 cars will carry more than 1075 people? (Hint: Restate this event in terms of the mean number of people x-bar per car.)</p></li>
<li><p>High school dropouts make up 14.1% of all Americans aged 18 to 24. A vocational school that wants to attract dropouts mails an advertising flyer to 25,000 persons between the ages of 18 and 24.
a)If the mailing list can be considered a random sample of the population, what is the mean number of high school dropouts who will receive the flyer?
b) What is the probability that at least 3500 dropouts will receive the flyer?</p></li>
</ol>
<p>Please help me on these problems, these are worth 5 grades, so it really counts a lot and these are the only six I’m having a problem with!</p>