"You are going to make a trash bin with a square base , vertical sides and no top. If you have 108 ft2 of material available, de
1 answer:
<h2>Dimension of trash bin is 6 ft x 6 ft x 3ft .</h2>
Step-by-step explanation:
Let h be the height of box and a be the side of base square.
We have 108 ft² material.
Surface area of trash bin = 108 ft²
Surface area of trash bin = a² + 4 ah
a² + 4 ah = 108
4ah = 108 - a²
Volume of trash bin, V = a²h
At maximum volume differentiation of volume will be zero
Surface area of trash bin = a² + 4 ah = 108
36 + 4 x 6 x h = 108
h = 3 ft
Dimension of trash bin is 6 ft x 6 ft x 3ft .
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Answer:
a) The company should expect to replace 11.51% of its batteries.
b) 35 months.
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 problem, we have that:
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. Then
has a pvalue of 0.1151.
The company should expect to replace 11.51% of its batteries.
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
To the nearest month, 35 months.