# We know that p hat is aan statistic because the mean

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We know that p-hat is a/an _______________ statistic because the mean of the sampling distribution of p-hat is equal to the true population proportion p. 3. According to the manufacturer’s specifications, the mean time required for a particular anesthetic drug to produce unconsciousness is 7.5 minutes with a standard deviation of 1.8 minutes. A random sample of 36 patients is to be selected and the average time for the drug to work will be computed for the sample. Find the probability that (a) the mean time for the sample will be less than 7.0 mins (b) a randomly selected patient requires less than 7.0 (c) If more random samples of size 36 were selected, the middle 95% of the sample means should fall between _______________ minutes and ______________ minutes. 4. As we have discussed in class, a one-pound (16 ounce) box of sugar generally weighs more than 1 lb. According to some state laws, producers will be fined if the mean of 5 randomly selected boxes is less than 1 lb. If the packaging equipment delivers individual weights that are N (μ, 0.4) ounces, what setting should be used for μ so the probability of being fined is 0.01? Provide a sketch to support your answer. 5. According to the __________________________________, when a simple random sample of size n is drawn from any population with mean µ and standard deviation σ, if n is sufficiently large the sampling distribution of the sample mean is approximately normal. 6. Place the word “true” or “false” in the blank at the end of each of the following sentences. (a) If the underlying population is skewed, the distribution of x-bar will be normal for n = 2. _________________ (b) If the underlying population is skewed, the distribution of x-bar will be normal for n = 100. ________________ (c) If the underlying population is normal, the distribution of x-bar will be normal for n = 2. _________________ (d) If the underlying population is normal, the distribution of x-bar will be normal for n = 100. ________________ 7. We know that 60% of the students in a large state university are male. (a) Determine the mean and standard deviation of the sampling distribution of the sample proportion of males (p-hat) when samples of 400 students are randomly selected from this population. (b) Verify that the formula you used for your standard deviation computation is valid in this situation. State the condition(s) that must be satisfied and convince me that all necessary conditions are met. (c) What is the probability that a simple random sample of 400 students will contain more than 65% males? 8. The weight of eggs produced by a certain breed of hen is N (60, 4). What is the probability that the weight of a dozen (12) randomly selected eggs falls between 700 grams and 725 grams.
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