James is supposed to take medication every night, but sometimes he forgets. He forgets to take his medication 3% of the time. Let X be the number of days next month (December) that James forgets to take his medication at night. X has a binomial distribution with parameters n = 31 and p = 0.03. Suppose we wanted to determine the chance James remembers to take his medication on exactly 27 days in December. Thus, we would be seeking P(X = ). What is the chance James forgets to take his medication exactly once in December? P(X = 1) = % Express answer as a percent, rounded to the nearest integer. What is the chance James forgets to take his medication fewer than two times in December?

X is normally distributed with ?=14 and ?= 4.   Find the probability that x is between 1 and 18.

From the help of following image, show every formula used for each step in excel..

An organization believes that the thought of adults ages 55 and over on which industry has the most trustworthy advertising is uniformly distributed. To test this claim, you randomly select 800 adults age 55 and over and ask each which industry has the most trustworthy advertising. The results are shown in the table. At a= 0.05, can you reject the claim that the distribution is uniform (i.e., that each frequency should be the same- in this case, 160, since there are 800 total adults sampled)? Explain. Response                                 Frequency, f        Auto Companies                              128 Fast food Companies                       192 Financial Service Companies            112 Pharmaceutical Companies              152 Soft Drink Companies                       216

According to Reader's Digest,  44% of primary care doctors think their patients receive unnecessary medical care. Use the z-table. a. Suppose a sample of 260 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their patients receive unnecessary medical care. E(p)=  (to 2 decimals)    (to 4 decimals) b. What is the probability that the sample proportion will be within  ±0.03 of the population proportion? Round your answer to four decimals.   c. What is the probability that the sample proportion will be within ±0.05  of the population proportion? Round your answer to four decimals.   d. What would be the effect of taking a larger sample on the probabilities in parts (b) and (c)? Why? The probabilities would - Select your answer -increasedecreaseItem 5 . This is because the increase in the sample size makes the standard error, ,