Answer to Question #317376 in Statistics and Probability for cosette

Question

ACTIVITY 2:  APPLY THE CENTRAL LIMIT THEOREM

1. A Neilsen reported that children between the ages 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours.

2. Assume that the mean systolic blood pressure of normal adults is 120 milliliters of mercury (mmHg) and the standard deviation is 5.6. If the sample of 30 adults is randomly selected, find the probability that the sample mean will be between 120 and 121.8 mmHg. Assume that the variable is normally distributed.

Answer 1

P(Z>26.3)=0.5-P(25<Z<26.3)

$(\frac{25-25}{3/\sqrt{20}}<Z<\frac{26.3-25}{3/\sqrt{20}})=(0<Z<1.94)$

P(25<Z<26.3)=0.9738-0.5=0.4738

P(Z>26.3)=0.5-0.4738=0.0262

2.$P(120<Z<121.8)=P(\frac{120-120}{5.6/\sqrt{30}}<Z<\frac{121.8-120}{5.6/\sqrt{30}})=P(0<Z<1.76)$

P(120<Z<121.8)=0.9608-0.5=0.4608