20. The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. Let X = average percent of fat calories.
a. For the group of 16, find the probability that the average percent of fat calories consumed is more than 5 ___________Answer
b. Find the first quartile for the average percent of fat calories. Round answer to two decimal places (i.e. 1.23) __________Answer
mean, mu = 36
std. dev. sigma = 10
Here population std. dev. is given, hence we can use z-values to calculate the probability as per central limit theorem.
z = (xbar - mu)/(sigma/sqrt(n))
a)
P(X > 5)
= P(z > (5 - 36)/(10/sqrt(16)))
= P(z > -12.4)
= 1
This value of z is very extreme to the left, hence probability to its right is 1
b)
lets find the value of z which represents the first quartile in the
normal curve
P(z < -0.67) = 0.25
z = -0.67
x = 36 -0.67*10/sqrt(16)
x = 34.33
20. The percent of fat calories that a person in America consumes each day is normally...
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. (a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places) (b) Find the first quartile for the percent of fat calories. (c) Find the first quartile for the...
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. (a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places) (b) Find the first quartile for the percent of fat calories. (Round to 4 decimal places) (c) Find...
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. (a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places) (b) Find the first quartile for the percent of fat calories. (Round to 4 decimal places) (c) Find...
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen. (a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places) QUESTION 14 4 points Save Answer (b) Find the first quartile for the percent of fat calories. QUESTION...
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