MAT 133 Assignment Solutions 2023 (MATH)

MAT 133 Assignment Solutions 2023 (MATH)Freshman class at Big State totaled 5,348 students. Of those, 1,263 received a merit scholarship. The merit scholarship amounts were normally distributed with a mean of $3,441 and standard deviation of $485. If the full tuition cost was $4,250 last year, what percentage of students who received a merit scholarship did NOT receive enough to cover full tuition. They tell us that the merit scholarships had a mean of µ=$3,441 and a standard deviation of s =$485. So some students received more and some received less, but the average received is $3,441. They are asking us how many received less than $4,250. If you received less than $4,250, it means that you can’t cover tuition. Here we introduce NORM.DIST in Excel. To figure out the area to the left of the normal curve to the left of a particular value we enter the x-value, the mean (µ), and the standard deviation (s), into: =NORM.DIST(x, µ, s, 1) From the problem: µ = $3,441, s = $485, x = $4,250 P(x < 4250) =NORM.DIST(4250, 3441, 485, 1) = .9523 ≈ 95% won’t receive enough to cover full tuition). Here is what it looks like in Excel: