  The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36and a standard deviation of 9 Suppose that one individual is randomly chosen Let X percent of fat calories. Round allanswers to 4 decimal places if where possiblea. What is the distribution of X?X ~ N(b. Find the probability that a randomly selected fat calorie percent is more than 33.c. Find the minimum number for the upper quarter of percent of fat calories.

Question help_outlineImage TranscriptioncloseThe 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 9 Suppose that one individual is randomly chosen Let X percent of fat calories. Round all answers to 4 decimal places if where possible a. What is the distribution of X?X ~ N( b. Find the probability that a randomly selected fat calorie percent is more than 33. c. Find the minimum number for the upper quarter of percent of fat calories. fullscreen
Step 1

Given that percent of fat calories that a person consumes in America each day is normally distributed with mean 36 and standard deviation 9.

It is said that one individual is randomly selected .

The central limit theorem states that if you have a population with mean μ and standard deviation σ and with  large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed with mean μ and standard deviation σ/√n. where n is sample size.

Here we know population mean μ = 36

population standard deviation = σ = 9

here one individual is selected so sample size n = 1.

So sample mean = 36 and sample standard deviation = σ/√n = 9/√1 = 9.

So X is normally distributed with mean 36 and variance 9^2 = 81. - N(36,81)

Step 2

We need probability that randomly selected fat percentage is more than 33.

We need P(X > 33) we write in terms of Z score as we know X - N(36,81), we get ...

Want to see the full answer?

See Solution

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Statistics 