Question

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about   45   and a standard deviation of   7.5 . Suppose that one individual is randomly chosen. Let   X=   percent of fat calories.

In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest   0.01 .

1. (.25)   X∼    (pick one) UBNE   (    ,    ) .
   
2. 
   
3. (.25) The probability that a person consumes more than   40   percent fat is    .
   
4. 
   
5. (.25) What is the lowest quartile for percent of fat calorie consumption?    .
   
6. 
   
7. (.25) Write the probability statement for part (c):   P(X  (pick one) <>=   )=  .
   

Problem 3

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of   180   feet and a standard deviation of   60 feet. Let   X=   distance in feet for a fly ball.

In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest   0.01 .

1. (.3)   X∼    (pick one) BNUE   (    ,    ) .
   
2. 
   
3. (.35) For a random fly ball, what is the probability that this ball traveled fewer than   220   feet?   P(X<220)=    .
   
4. 
   
5. (.35) The   80th   percentile of the distribution of fly balls is given by   P(X<  )=0.80 .
   

Problem 4

Four-year-olds in China average   3   unsupervised hours per day. Most of the unsupervised children live in rural areas, considered safe. Suppose that the amount of unsupervised time is normally distributed with standard deviation   1.5 . A Chinese 4-year-old is randomly selected from a rural area. We are interested in the amount of time the child spends alone per day.

In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest   0.01 .

1. (.25) In words, the random variable   X   in which we are interested is defined by   X=  (pick one) time spent alonenumber of 4-year oldsnumber of rural areas .
   
2. 
   
3. (.25) Find the probability that the child spends less than one hour per day unsupervised.   P(X<1)=  .
   
4. 
   
5. (.25) What is the probability that the child will spend over ten hours per day unsupervised.   P(X>10)=  .
   
6. 
   
7. (.25) The   70th   percentile of the distribution of unsupervised time is given by   P(X<  )=0.70 .
   

Answer 1

Mean = 45  

Standard deviation = 7.5

The probability that a person consumes more than   40 per cent fat is

What is the lowest quartile for per cent of fat calorie consumption?