Question

A soft drink machine outputs a mean of 28 ounces per cup. The machine's output is normally distributed with a standard deviation of 2 ounces. What is the probability of filling a cup between 26 and 31 ounces? Round your answer to four decimal places.

Answer 1

the probability of filling a cup between 26 and 31 ounces is 0.7745

Explanation:

Step 1: Sketch the curve.

The probability that 26<X<31 is equal to the blue area under the curve.

Step 2:

Since μ=28 and σ=2 we have:

P ( 26<X<31 ) = P ( 26−28 < X−μ < 31−28 )

⇒ P ( (26−28)/2 < X−μ/σ < (31−28)/2 )

Since Z= x−μ/σ , (26−28)/2 = −1 and (31−28) / 2 = 1.5 we have:

P ( 26<X<31 )=P ( −1<Z<1.5 )

Step 3: Use the standard normal table to conclude that:

P ( −1<Z<1.5 )=0.7745

Therefore , the probability of filling a cup between 26 and 31 ounces is 0.7745