Question

This Question: 5 pts 2 of 14 (D complete)w This Quiz: 67 pts possible EQuestion Help A study discovered that Americans consumed an average of 10.4 pounds of chocolate per year. Assume that the annual chocolate consumption follows the nomal 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 chooolate next year? (Round to four decimal places as needed.) b. What is the probablity that an American will consume more than 8 pounds of chooolate next yearh Round to four decimal places as needed) e. What is the probability that an American will consume between 7 and 11 pounds of chooolate next year? (Round to four decimal places as needed.) d. What is the probability that an American will consume exactly 9 pounds of chooolate next year? (Round to four decimal places as needed) e. What is the annual consumption of chooolate that represents the 60th percentle? pounds of chooolate The 60th percentile is represented by an annual consumption of (Type an integer or decimal rounded to one decimal place as needed )

Answer 1

Mean = $\mu$ = 10.4

Standard deviation = $\sigma$ = 3.7

a)

We have to find P(X < 6)

For finding this probability we have to find z score.

$z =\frac{x-\mu}{\sigma} =\frac{6-10.4}{3.7}=-1.19$

That is we have to find P(Z < - 1.19)

P(Z < - 1.19) = 0.1172

( From z table)

b)

We have to find P(X > 8)

For finding this probability we have to find z score.

$z =\frac{x-\mu}{\sigma} =\frac{8-10.4}{3.7}=-0.65$

That is we have to find P(Z > - 0.65)

P(Z > - 0.65) = 1 - P(Z < - 0.65) = 1 - 0.2583 = 0.7417

( From z table)

c)

We have to find P( 7 < X < 11)

For finding this probability we have to find z score.

$z =\frac{x-\mu}{\sigma} =\frac{7-10.4}{3.7}=-0.92$

$z =\frac{x-\mu}{\sigma} =\frac{11-10.4}{3.7}=0.16$

That is we have to find P( - 0.92 < Z < 0.16)

P(Z < 0.16) - P(Z < - 0.92) = 0.5644 - 0.1791 = 0.3853

( From z table)

d)

P(X = 9) = 0

( Because X follows normal distribution and it is countinuous so probability of exact number is zero)

e)

We have given P(X < x) = 0.60

z value for 0.60 is 0.25

We have to find value of x

$x=\mu&plus;z*\sigma=10.4&plus;0.25*3.7=11.3$

The 60th percentile is represented by annual consumption of 11.3 pounds of chocolate.