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Question

Ivy finishes each puzzle with a normal distribution of times where μ = 6 minutes and σ = 14 minutes.

Determine the probability of 22 completed puzzles having an average of 10 minutes or shorter.

Answer 1

Let μ = 6 and σ = 14. Use the z-score formula to find the probability of completing 22 puzzles in 10 minutes or less.

σ_x-bar = σ/n = 14/√22= 2.98 (sample standard deviation)

z = (10 - 6) / 2.98 = 1.34

Use the z-score table to find the probability. P(z < 1.34) = 0.9099.

The probability of 22 completed puzzles having an average of 10 minutes or shorter is 0.9099.