Question 5 (1 point)
Factory made chocolate chip cookies will have a mean weight of 42 grams. The weight is normally distributed and for quality control, the
standard deviation is 1.5 grams. Cookies that weigh more than 45 grams or less than 39 grams are rejected. How many cookies wil be rejected
in a 5,000 count batch of cookies?

228 cookies wil be rejected in a 5,000 count batch of cookies.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Proportion of rejected cookies.

Less than 39:

pvalue of Z when X = 39.

has a pvalue of 0.0228.

More than 45:

1 subtracted by the pvalue of Z when X = 45.

has a pvalue of 0.9772

1 - 0.9772 = 0.0228

Total:

2*0.0228 = 0.0456

How many cookies wil be rejected in a 5,000 count batch of cookies?

The proportion of cookies rejected is 0.0456. Out of 5000:

0.0456*5000 = 228

228 cookies wil be rejected in a 5,000 count batch of cookies.

8 2/3 is the answer

step-by-step explanation: just use a calculator

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.