A study discovered that Americans consumed an average of 10.3 pounds of chocolat
ID: 3338390 • Letter: A
Question
A study discovered that Americans consumed an average of 10.3 pounds of chocolate per year Assume that the annual chocolate consumption follows the normal distribution with a standard deviation of 3.7 pounds. Complete parts a through e below. a. What is the probability that an American will consume less than 6 pounds of chocolate next year? (Round to four decimail places as needed) b. What is the probability that an American will consume more than 8 pounds of chocolate next year? (Round to tour decimal places as needed ) c. What is the probability that an American will consume between 7 and 11 pounds of chocolate next year? (Round to four decimal places as needed) d. What will consume exactly 9 pounds of chocolate next year? (Round to four decimal places as needed.) e. What is the annual consumption of chocolate that represents the 80th percentile? The 80th percentile is represented by an annual consumption of pounds of chocolate. s the probability that an American Type an integer or decimal rounded to one decimal place as needed)Explanation / Answer
Formula: Z = (X-mean)/s
a) P(X < 6) = P(Z < (6-10.3)/3.7) = P(Z < -1.16) = 0.1230
b) P(X > 8) = P(Z > (8-10.3)/3.7) = 1 - P(Z < -0.62) = 0.7324
c) P7 < X < 11) = P(X < 11) - P(X < 7) = P(Z < (11-10.3)/3.7) - P(Z < (7-10.3)/3,7) = P(Z < 0.19) - P(Z < -0.89) = 0.3886
d) P(X = 9) = 0
e) P(Z < z) = 0.8
z = 0.84
0.84 = (x - 10.3)/3.7), x = 13.4
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