Question

Suppose that daily calorie consumption for American men follows a normal distribution with a mean of 2760 calories a standard deviation of 500 calories

a: On a randomly selected day, we would expect 90% of American men to consume ______ calories or more

  

Answer 1

Solution :

Given that ,

mean = = 2760

standard deviation = = 500

The z - distribution of the 90% is,

P( Z > z ) = 90%

1 - P( Z < z ) = 0.90

P( Z <  ) = 1 - 0.90

P( Z < z ) = 0.10

P( Z < -1.28 ) = 0.10

z = -1.28

Using z - score formula,

X = z * +

= -1.28 * 500 + 2760  

= 2120

On a randomly selected day, we would expect 90% of American men to consume 2120 calories or more.