When a truckload of apples arrives at a packing plant, a random sample of 125 apples are selected and examined for bruises and other defects. In reality, 9% of the apples on a particular truck are bruised or otherwise unsatisfactory. (a) How many standard errors away from 0.09 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find

The number of standard errors is given by the Zscore, hence, the sample proportion containing 89% of the bad apples would be 1.6 standard deviations from the mean.

89th percentile can be interpreted as :

The Zscore gives the number of standard deviations a certain score or proportion is from the mean.

Using a normal distribution table :

Therefore, about 1.6 standard errors from the mean would contain 89% of the proportion of bad Apples.

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You would need to go 1.6 standard errors away from 0.09.

Step-by-step explanation:

We can solve this using the normal distribution, because, by the Central Limit Theorem, the sampling distribution of the sample proportions is approximately normal.

Problems of normally distributed samples are 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.

89% of the sample proportions.

50 - 89/2 = 5.5th percentile

50 + 89/2 = 94.5th percentile

5.5th percentile

X when Z has a pvalue of 0.055. So X when Z = -1.6.

So 1.6 standard error away from 0.09.

94.5th percentile

X when Z has a pvalue of 0.945. So X when Z = 1.6.

So 1.6 standard error away from 0.09.

You would need to go 1.6 standard errors away from 0.09.

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.