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Soloha48 [4]
3 years ago
7

My Notes A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1600 hours and

a standard deviation of 70 hours. To minimize the number of bulbs that burn out during operating hours, all bulbs are replaced at once. How often should the bulbs be replaced so that no more than 1% burn out between replacement periods? (Round your answer to one decimal place.)
Mathematics
1 answer:
Evgen [1.6K]3 years ago
6 0

Answer:

The bulbs should be replaced each 1436.9 hours.

Step-by-step explanation:

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

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 1600, \sigma = 70

How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?

This is the first percentile of hours. So it is X when Z has a pvalue of 0.01.

So it is X when Z = -2.33.

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

-2.33 = \frac{X - 1600}{70}

X - 1600 = -2.33*70

X = 1436.9

The bulbs should be replaced each 1436.9 hours.

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mrs_skeptik [129]
Answer (5/264,76/33)
5 0
2 years ago
Length and breadth of a rectangular field is 5 : 3. If the breadth of rectangle is 60m, find the length of the rectangle.
djverab [1.8K]

Answer:

5m

Step-by-step explanation:

Given data

Ratio of length to breadth is 5 : 3

hence in fraction form it is 5/3

the breadth of rectangle is 60m

let the length be x

So

5/3= x/3

cross multiply we have

5*3= 3x

15= 3x

divide both sides by 3

x= 15/3

x= 5m

Hence the length is 5m

3 0
3 years ago
HHHHELP ME!!!!!! PLZ
Brilliant_brown [7]

Total gasoline = 10 gallons

Gasoline left after 100 miles = 5 gallons

Gasoline used in 100 miles

= Total gasoline - Gasoline left after 100 miles

= 10 gallons - 5 gallons

= 5 gallons

Gasoline used in 1 mile

= Gasoline used in 100 miles/100

= 5 gallons/100

= 0.05 gallons

8 0
2 years ago
Your surf shop sells two types of surfboards. The first type A, costs $272 and you make a profit of $29 on each one. The second
brilliants [131]
Let the number of type A surfboards to be ordered be x and the number of type B surfboards be y, then we have

Minimize: C = 272x + 136y

subject to: 29x + 17y ≥ 1210
                 x + y ≤ 50
                 x, y ≥ 1

From the graph of the constraints, we have that the corner points are:

(20, 30), (41.138, 1) and (49, 1)

Applying the corner poits to the objective function, we have

For (20, 30): C = 272(20) + 136(30) = 5440 + 4080 = $9,520
For (41.138, 1): C = 272(41.138) + 136 = 11189.54 + 136 = $11,325.54
For (49, 1): C = 272(49) + 136 = 13328 + 136 = $13,464

Therefore, for minimum cost, 20 type A surfboards and 30 type B surfboards should be ordered.
6 0
3 years ago
3.) Simplify the expression.
Bogdan [553]

Answer:

Option C) -cosu is correct

Therefore the simplified expression is cos(u+\pi)=-cosu

Step-by-step explanation:

Given expression is cos(u+\pi)

To find the value of the given expression :

By using the formula cos(A+B)=cosAcosB-sinAsinB

Substitute A=u and B=\pi in the above formula we get

cos(u+\pi)=cosucos\pi-sinusin\pi

=cosu(-1)-sinu(0)  ( here cos\pi=-1 and sin\pi=0 )

=-cosu-0

=-cosu

cos(u+\pi)=-cosu

Therefore option C) -cosu is correct

Therefore the simplified expression is cos(u+\pi)=-cosu

6 0
3 years ago
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