# Easy Stats Question

The z-score for \$30,000 = (\$30,000 – \$40,000) / \$7,500 or –1.3333, which corresponds with 0.0918. The z-score for \$35,000 = (\$35,000 – \$40,000) / \$7,500 or –0.6667, which corresponds with 0.2514. The difference is 0.1596 or 15.96%. In these calculations, where do the “corresponding” numbers come from? If I look at the z-table, I get .4082 for the first one, and .2454 for the second one. I know this is probably something simple…thanks for the help

Monthly sales of hot water heaters are approximately normally distributed with a mean of 21 and a standard deviation of 5. What is the probabilility of selling 12 hot water heaters or less next month? A) 1.80%. B) 3.59%. C) 96.41%. D) 98.2%. Your answer: A was incorrect. The correct answer was B) 3.59%. Z = (12 – 21) / 5 = -1.8 From the cumulative Z-table, the probability of being more than 1.8 standard deviations below the mean, probability x < -1.8, is 3.59%. Also, on this one, why don’t they divide the answer by two? Don’t you have to divide to take out the area above 1.8 deviations?

0.5 - 0.4082 = 0.0918 0.5 - 0.2454 = 0.2546 Does that help?

hoffmag2 Wrote: ------------------------------------------------------- > Monthly sales of hot water heaters are > approximately normally distributed with a mean of > 21 and a standard deviation of 5. What is the > probabilility of selling 12 hot water heaters or > less next month? > > > A) 1.80%. > > B) 3.59%. > > C) 96.41%. > > D) 98.2%. > > > Your answer: A was incorrect. The correct answer > was B) 3.59%. > > Z = (12 – 21) / 5 = -1.8 > > From the cumulative Z-table, the probability of > being more than 1.8 standard deviations below the > mean, probability x < -1.8, is 3.59%. > > > Also, on this one, why don’t they divide the > answer by two? Don’t you have to divide to take > out the area above 1.8 deviations? This is a probability question. You are doing some p-vaalue calculation for a test statistic.

you are looking at scores between 0 and the z value so you are look at + 1.33 - getting .4082 when you need -1.33 -> value would be .5-.4082 = .0918 similarly for -.67 --> value would be 0.5 - .2486 = .2514

I guess I’m just confused by the math - I was assuming that by taking x - y I would get the same thing as (.5 - y) - (.5 - x) .5 - y - .5 + x x - y My answer was close (got the question right) but it was still like .4 off…where am I screwing this thing up? WAIT - Looked at the wrong Z stat - Used the one for .66 rather than .67… I’m an idiot.