Question

1, A personal trainer at a gym is preparing a protein shake for a client after a work-out. The protein shake requires a 35 g serving of protein powder, to be taken from the
1.1 kg tub. If the tub in use is only partially full, and the amount remaining is unknown, what is the probability that there is enough protein powder left in the tub to make the protein shake?

P(X > 35)=P(X > 35)=

Round to 3 significant digits.

2. Find the z-values corresponding to the given measures of position, assuming that Z is a continuous random variable that follows a standard normal distribution.

Standard Normal Distribution Table

a. The range of values of the top 7% of the data.

z >

b. The range of values of the middle 80% of the data.

< z <

Answer 1

In order to solve question 1, can you please provide mean and variance of the protein powder.

Que.2

a.

We have to find z' such that,

P(z > z') = 0.07

Hence P(z < z') = 1- 0.07 = 0.93 --------- (1)

Now using standard normal table, P(z < 1.48) = 0.93  

Compare this equation with equation (1), we get z' = 1.48

Hence P( z > 1.48 ) = 0.07

b.

If the given values cover middle 80% area then remaining area is 100 - 80 = 20

This area is divided in two parts, below the selected region and above the selected region.

  

Area below the given region is 0.10.

From standard normal table ,

P(z < -1.28 ) = 0.10 and P( z > 1.28 ) = 0.10

Hence

P( -1.28 < z < 1.28 ) = 0.80