The weight of turkeys is normally distributed with a mean of

The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. Use Table 1. a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds.(Round z value to 2 decimal places and final answer to 4 decimal places.) Probability b. Find the probability that a randomly selected turkey weighs below 12 pounds. (Round your answer to 4 decimal places.) Probability

Solution

a. Convert 20 and 26 to z scores using the formula:
z = (x - mean)/sd

z = (20 - 22)/5 = -.4

z = (26 - 22)/5 = .8

P(20 < x < 26) = P(-.4 < z < .8) = P(z < .8) - P(Z < -.4) = .7881 - .3446 = .4435

answer: 0.4435

z = (12 - 22)/5 = -2

P(x < 12) = P(Z < -2) = 0.0228

answer: 0.0228