Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p=0.2. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. P(X< 4) = (Round to four decimal places as needed.)

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 38 who smoke. Step 1 of 2:  Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, estimate the proportion of Americans over 38 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.   Step 2 of 2:  Suppose a sample of 273 Americans over 38 is drawn. Of these people, 79 smoke. Using the data, construct the 85% confidence interval for the population proportion of Americans over 38 who smoke. Round your answers to three decimal places.   Lower end point, upper end point

If most of the scores in a large data set are about close together except for a few scores that are quite a bit higher, how would the mean and median of the data set compare and what shape would a histogram of the data set have? The mean would be smaller than the median and the histogram would be skewed with a long tail towards higher scores. The mean would be larger than the median and the histogram would be skewed with a long tail towards lower scores. The mean would be smaller than the median and the histogram would be skewed with a long tail towards lower scores. The mean would be larger than the median and the histogram would be skewed with a long tail towards higher scores. The mean would be equal to the median and the histogram would be symmetrical. None of the answers listed.

You are a paranoid delusional statistician with far too much time on your hands. One day, you sit down to have a bowl of soup. This bowl of soup happens to be Tic-Tac-Toe themed, meaning that you have some noodles that are shaped like an X, and some that are shaped like an O. As you stir your soup, you notice that this bowl seems to have a particularly high number of X- shaped noodles in it. Being paranoid, you conclude that this has some meaning like someone is trying to give you a message, possibly warning you of the dangers of x-rays. You jump out of your seat and run to get your x-ray-proof cape, and then you pause for a moment and think that you should calculate a chi-square statistic for the frequency of X-shaped noodles before freaking out. First, you carefully separate each of the noodles by shape and count them. Here is what you find: Frequency of Noodles X-shaped 33 O-shaped 21 2. Write out the null and alternative hypotheses using symbols: Но: На:

Please answer part a-d. please show all your work