A company produces packets of soap powder labeled "Giant size 32 Ounces." The actual weight of soap powder in a box has a normal distribution with a mean of 33 oz. And a standard deviation of 0.8 oz. The proportion of packets that are underweight (i. E. Weight less than 32 oz.) are

0.1057

Step-by-step explanation:

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score = 32 oz

μ is the population mean = 33 oz

σ is the population standard deviation = 0.8oz

For x < 32 oz

z = 32 - 33/0.8

z = -1.25

Probability value from Z-Table:

P(x<32) = 0.10565

Approximately = 0.1057

Therefore, the proportion of packets that are underweight (i.e. Weight less than 32 oz.) are 0.1057.

idk

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240