Exercises on The Central Limit Theorem

1. Under what conditions can the Central Limit Theorem be used?

  Only on alternate Tuesdays.
  When n < 30 and the original population is normal.
  For n > 30 and any original population.
  Both answer b and c apply .

2. According to our text, the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. According to Dr. Whiteford of Essex Community College's Physican's Assistant Program, a birth is considered to be pre-term if the pregnancy lasts less than 262.5 days. If 40 pregnancies are randomly selected, what is the probability that the mean length of their pregnancies is less than 262.5 days?

  P( < 262.5) = 5.05%.
  P( < 262.5 ) = 48.98%.
  P( < 262.5 ) = 98.98%.
  P( < 262.5 ) = 1.02%.

3. According to our text, the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. According to Dr. Whiteford of Essex Community College's Physican's Assistant Program, a birth is considered to be post-due-date if the pregnancy last more than 294 days. If 31 pregnancies are randomly selected, what is the probability that their mean length of pregnancy is more than 294 days?

  P( > 294 ) = 12.17%.
  P( > 294 ) = 0.01%.
  P( > 294 ) = 62.17%.
  P( > 294 ) = 87.83%.

4. Heights of men are normally distributed with a mean of 69 in. and a standard deviation of 2.8 in. (based on data from the National Health Survey). If 35 men are randomly selected, what is the probability that their mean height is less than 70.0 in.?

  P( < 70) = 35.00%.
  P( < 70) = 1.74%.

  P( < 70) = 48.26%.

  P( < 70) = 98.26%.

5. According to our text, the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. In a random sample of 35 women, what is the probability that their mean pregnancy is greater than 270 days?

  P( > 270) = 78.52%.
  P( > 270) = 21.48%.
  P( > 270) = 28.52%.
  P( > 270) = 50.00%.

6. Heights of women are normally distributed with a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the National Health Survey). If 50 women are randomly selected, what is the probability that their mean height is less than 60.0 in.?

  P( < 60) = 99.99%.
  P( < 60) = 0.01%.
  P( < 60) = 10.18%.
  P( < 60) = 49.99%.