7 total questions exploring Discrete Random Variables and Normal Distribution. Please show all steps when solving the problems.

1. Multiple choice questions each have 6 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions. What is the probability of getting exactly one correct answer when 5 guesses are made?

2. Pretty Betty has a share of 28. 28% of households were tuned to Pretty Betty. Assume an advertiser verifies 28% survey with 15 households. Find probability that at most one household is tuned to Pretty Betty. P(at most one).

3. Assume that a procedure yields a binomial distribution with n=405 trials and the probability of success for one trial is p=0.59. Use the range rule of thumb to find minimum usual value of mean -2 standard deviations and the maximum usual value of the mean + 2 standard deviations.

4. Several anthropologist students were unprepared for a true/false quiz with 15 questions. All answers were guesses. Give the range for the usual number of correct answers.

5. CIA analyze frequencies of letters used to decipher intercepted messages. The letter o is used at a rate of 7.16%. Give the interval of usual values for the number of o's appearing on a page of 2900 characters.

6. Reading on a thermometer are normally distributed with a mean of 0 degrees celsius and a standard deviation of 1.00 degrees celsius. Thermometer was randomly selected. Find the probability of obtaining a reading between -2.557 degrees celsius and 0.114 degrees celsius. P (-2.557

7. Pregnancies in a small rural village normally distributed with a mean of 270 days and a standard deviation of 12 days. What percentage of pregnancies las beyond 269 days? P(X>269).