# Question: Let x denote the duration of a randomly selected pregnancy

Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standard deviation of x are 266 days and 16 days, respectively. Suppose that a normal distribution is an appropriate model for the probability distribution of x.

a. What is the probability that the duration of pregnancy is between 250 and 300 days?

b. What is the probability that the duration of pregnancy is at most 240 days?

c. What is the probability that the duration of pregnancy is within 16 days of the mean duration?

d. A Dear Abby column dated January 20, 1973, contained a letter from a woman who stated that the duration of her pregnancy was exactly 310 days. (She wrote that the last visit with her husband, who was in the navy, occurred 310 days before the birth.) What is the probability that the duration of a pregnancy is at least 310 days? Does this probability make you a bit skeptical of the claim?

e. Some insurance companies will pay the medical expenses associated with childbirth only if the insurance has been in effect for more than 9 months (275 days). This restriction is designed to ensure that the insurance company has to pay benefits only for those pregnancies for which conception occurred during coverage. Suppose that conception occurred 2 weeks after coverage began. What is the probability that the insurance company will refuse to pay benefits because of the 275-day insurance requirement?

a. What is the probability that the duration of pregnancy is between 250 and 300 days?

b. What is the probability that the duration of pregnancy is at most 240 days?

c. What is the probability that the duration of pregnancy is within 16 days of the mean duration?

d. A Dear Abby column dated January 20, 1973, contained a letter from a woman who stated that the duration of her pregnancy was exactly 310 days. (She wrote that the last visit with her husband, who was in the navy, occurred 310 days before the birth.) What is the probability that the duration of a pregnancy is at least 310 days? Does this probability make you a bit skeptical of the claim?

e. Some insurance companies will pay the medical expenses associated with childbirth only if the insurance has been in effect for more than 9 months (275 days). This restriction is designed to ensure that the insurance company has to pay benefits only for those pregnancies for which conception occurred during coverage. Suppose that conception occurred 2 weeks after coverage began. What is the probability that the insurance company will refuse to pay benefits because of the 275-day insurance requirement?

## Answer to relevant Questions

Let x denote the systolic blood pressure of an individual selected at random from a certain population. Suppose that the normal distribution with mean m 5 120 mm Hg and standard deviation σ = 10 mm Hg is a reasonable model ...A random sample is selected from a population with mean m = 100 and standard deviation s = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes: a. n 5 9 d. n 5 ...Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10. a. What is the probability that the sample mean will be within 1 of the value of µ? b. For this example (n = 100, σ = 10), ...The article “Unmarried Couples More Likely to Be Interracial” (San Luis Obispo Tribune, March 13, 2002) reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population ...b. What is the probability that the sample mean is between 49.75 pounds and 50.25 pounds? c. What is the probability that the sample mean is less than 50 pounds?Post your question