Records suggest that the normal distribution with mean 67 and standard deviation 11 is a plausible model for a measurement of the amount of people in a subway coach. Find P [ 42.25 $\le$ X $\le$77.67 ].
A) .822
B) .821
C) .818
D) .814

Question

Quizplus · Accepted Answer

To find P[42.25 ≤ X ≤ 77.67], we calculate the z-scores for 42.25 and 77.67 using the formula z = (X - μ) / σ. For 42.25, z = (42.25 - 67) / 11 = -2.25. For 77.67, z = (77.67 - 67) / 11 = 0.97. Using standard normal distribution tables or a calculator, P(-2.25 ≤ Z ≤ 0.97) ≈ 0.822.

Records Suggest That the Normal Distribution with Mean 67 and Standard