2.Binomial, Poisson, Exponential and Normal distributions

2.1. Married- women study, chicken with contamination and marital name changing:

(i) According to Women's Day magazine (Jan. 2007), 50% of married women would marry their current husbands again if given the chance. Consider the number in a random sample of 12 married women who would marry their husbands again. Identify the discrete probability distribution that best models the distribution of . Explain.

(ii) The United States Department of Agriculture reports that, under its standard inspection system one in every 100 slaughtered chickens passes inspection for fecal contamination. Find the probability that, in a random sample of 6 slaughtered chickens, at least one passes inspection for fecal inspection.

(iii) As a female, how likely are you to follow tradition and change your last name to your husband's when you get married? This was one of the questions investigated in research published in Advances in Applied Sociology (Nov. 2013). According to the study, the probability that an American female will change her last name upon marriage is 0.9. Consider a sample of 25 American females: How many of these females would you expect to change their last name upon marriage? How likely is it that 20 or more of these females will change their last name upon marriage (calculate by hand and confirm the answer using MS Excel 'BINOMDIST' function)?

2.2. Airline fatalities and emergency room bed availability:

(i) US airlines average about 4.5 fatalities per month. Assume that the probability distribution for , the number of fatalities per month, can be approximated by a Poisson probability distribution. What is the probability that no fatalities will occur during any given month (calculate by hand and confirm the answer using MS Excel 'POISSONDIST' function)? Calculate the expected value and standard deviation of the fatalities per month.

(ii) The mean number of patients admitted per day to the emergency room of a small hospital is 2.7. If, on a given day, there are only four beds available for new patients, what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?

2.3. Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability (by hand and using MS Excel) that a call takes:

• 3 minutes or less.
• exceed 5 minutes.

2.4. To gauge their fear of going to a dentist, a random sample of adults completed the Modified Dental Anxiety Scale (MADA) questionnaire. Scores on a scale range from zero (no anxiety) to 25 (extreme anxiety). The mean score was 11 and the standard deviation was 4, i.e. a normal distribution with =11 and =4.

• Find the probability that someone scores between 10 and 15 on the MADA (by hand and using MS Excel).
• Find the probability that someone scores above 20 on the MADA.