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lara [203]
3 years ago
11

Cook-Easy blender has a mean time before failure of 41 months with a standard deviation of 4 months, and the failure times are n

ormally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the blenders returned
Mathematics
1 answer:
Naddika [18.5K]3 years ago
7 0

Answer:

The warranty period should be of 35 months.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 p-value, we get the probability that the value of the measure is greater than X.

Cook-Easy blender has a mean time before failure of 41 months with a standard deviation of 4 months

This means that \mu = 41, \sigma = 4

What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the blenders returned?

The warranty period should be the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.

Z = \frac{X - \mu}{\sigma}

-1.405 = \frac{X - 41}{4}

X - 41 = -1.405*4

X = 35.4

Rounding to the nearest integer, 35.

The warranty period should be of 35 months.

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Factor and find the zeros. z^2-z+56
Inessa [10]

Answer:

Sry its long but if your to lazy to look thru it here is the answer=   z = {-7, 8}

Step-by-step explanation:

Simplifying

z2 + -1z + -56 = 0

Reorder the terms:

-56 + -1z + z2 = 0

Solving:

-56 + -1z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.

(-7 + -1z)(8 + -1z) = 0

Subproblem 1

Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying:

-7 + -1z = 0

Solving:

-7 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1z = 0 + 7

-1z = 0 + 7

Combine like terms: 0 + 7 = 7

-1z = 7

Divide each side by '-1'.

z = -7

Simplifying:

z = -7

Subproblem 2

Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying:

8 + -1z = 0

Solving:

8 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0

0 + -1z = 0 + -8

-1z = 0 + -8

Combine like terms: 0 + -8 = -8

-1z = -8

Divide each side by '-1'.

z = 8

Simplifying:

z = 8

Solution

z = {-7, 8}

4 0
2 years ago
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