Question

The probability is 0.314 that the gestation period of a woman will exceed 9 months. In six human births, what is the probability that the number in which the gestation period exceeds 9 months is
a. Exactly three?
b. Exactly five?
c. At least five?
d. Between three and five, inclusive?
e. Determine the probability distribution of the random variable
X, the number of six human births in which the gestation period exceeds 9 months.
f. Identify the probability distribution of X as right skewed, symmetric, or left skewed without consulting its probability distribution or drawing its probability histogram.
g. Draw a probability histogram for X.
h. Use your answer from part (e) and Definitions 5.9 and 5.10 on pages 217 and 219, respectively, to obtain the mean and standard deviation of the random variable X.
i. Use Formula 5.5 on page 230 to obtain the mean and standard deviation of the random variable X.