Standard Normal Distribution
Use the table while answering the problem.
Jim Tree sells Christmas trees. The mean length of the trees purchased was 68 inches with a standard deviation of 10 inches. Jim wants to know what per cent of his sales were more than 84 inches tall. He can use the standard normal distribution to help him.
He asks, “what is the mean?” Mean = a0 inches
He thinks, “What is the expected distribution about the mean?” ( 38 inches 48 inches 58 inches 68 inches 88 inches 98 inches 108 inches. )
He thinks, “a1 % of the sales will be below 68 inches.”
But, he needs to know the percentage between 68 and 84 to add to that.
So, he calculates a z-score = (84 – 68) / 10 = a2, and finds the percentage associated with 1.6 in the table.
This is (to the nearest tenth) a3 %.
Now Jim knows that a4 % of his sales were 84 inches or less.
Therefore, the remaining a5% were more than 84 inches.
