Question

The masses of Burgerville's half-pounders are normally distributed. Of these burgere 7) 33% have masses greater than 253.52 g and 40.9% of them have masses less than 248.16 g.Find the mean and standard deviation of the half-pounder masses.

Answer 1

Find the z-scores corresponding to the listed masses and set up equations for finding the mean µ and standard deviation σ.

P(Z > z) = 0.33 ⇒ z = (253.52 - µ)/σ ≈ 0.4399

P(Z < z) = 0.409 ⇒ z = (248.16 - µ)/σ ≈ -0.2301

Solve for µ and σ. We can eliminate µ and get σ by combining

(253.52 - µ)/σ - (248.16 - µ)/σ ≈ 0.4399 - (-0.2301)

5.36/σ ≈ 0.67

σ ≈ 8.4

Then solving for µ, we find

(253.52 - µ)/8.4 ≈ 0.4399

253.52 - µ ≈ 3.6952

µ ≈ 249.83