The proportion of American births that result in a birth defect is approximately $1/33$ according to the Centers for Disease Control and Prevention (CDC). A local hospital randomly selects five births and lets the random variable X count the number not resulting in a defect. Assume the births are independent.
1. X follows a
A) Normal distribution with mean 5 and variance $1/33$.
B) binomial distribution with $n=5$ and $p=1/33$.
C) binomial distribution with $n=5$ and $p=32/33$.
D) None of the above
2. The mean and standard deviation of the distribution of X are closest to
A) 0.1515 and 0.1469.
B) 4.8485 and 0.3833.
C) 0.1515 and 0.3833.
D) 4.8485 and 0.1469.
3. What is the probability that two of the five births do not result in defects?
A) 0.0003
B) 0.0008
C) 0.0084
D) 0.3125
4. The probability that at least one of the births results in a defect is closest to
A) 0.0000.
B) 0.1426.
C) 0.8574.
D) 1.0000.
5. A researcher suggests using 500 births instead of only 5. In this case, the distribution of X can be reasonably approximated by
A) N(500, 1/33).
B) N(484.85, 1/33).
C) N(500, 3.83).
D) N(484.85, 3.83).
