Question

Americans receive an average of 17 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Answer the following, rounding probabilities to 4 decimals.

Let X = the number of Christmas cards received by a randomly selected American

a. The distribution is X ~ ( , )

b. What's the probability that a randomly chosen American received at least 25 Christmas cards?

c. What's the probability that a randomly chosen American received no more than 5 Christmas cards?

d. What's the probability that a randomly chosen American received between 20 and 30 Christmas cards?

e. The middle 80% of cards received are between cards and cards. Round answers to 2 decimals.

Answer 1

a) X ~ N(17, 6)

b)

=0.5-0.4082 =0.0918

Answer : 0.0918

c)

=0.5-0.4772 =0.0228

Answer: 0.0228

d)

= 0.4850-0.1915 =0.2935

Answer: 0.2935

e) For middle 80% the critical value of Z is +/-1.282

The Upper limit is

The lower limit is

Answer: The middle 80% of cards received are between 9.31 cards and 24.69 cards.