1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
What is the value of X enter your answer in the box
anyanavicka [17]

Answer:

x = 20

Step-by-step explanation:

The marked angles are vertical angles and congruent, thus

6x - 10 = 3x + 50 ( subtract 3x from both sides )

3x - 10 = 50 ( add 10 to both sides )

3x = 60 ( divide both sides by 3 )

x = 20

5 0
3 years ago
Read 2 more answers
If you wanted to reduce the 8 by a ratio of 1/4 what would the dimensions of the new rectangular be
kozerog [31]
Well you pay attention
8 0
3 years ago
Help please screenshot
Bingel [31]
48 cm. You have 16 units and know that 2 of them equal 6 cm. So you can either divide 16 by 2 and multiply by 6 or notice that each square is worth 3 cm and multiply 16 by 3 to get 48.
7 0
2 years ago
A is directly proportional to B when A=12 B=3 Find the value of A when B = 5​
Schach [20]

Answer:

A = 20

Step-by-step explanation:

12/3 = A/5

60 = 3A

A = 60÷3 = 20

3 0
2 years ago
(4 x 10) + (2 x 104)<br> Give your answer in standard form
Goshia [24]

Answer: =248x

Step-by-step explanation: Hope this help :D

Let's simplify step-by-step.

4x(10)+2x(104)

=40x+208x

Combine Like Terms:

=40x+208x

=(40x+208x)

=248x

7 0
3 years ago
Other questions:
  • Solve for x and y intercepts
    12·1 answer
  • I bought one more pound of apples than i did bananas. Apples cost $3.40/lb and bananas cost $2.30/lb. My total cost was $31.90.
    14·1 answer
  • Every Halloween, trick-or-treaters love going to Erica's house to see her spooky decorations and get some of her delicious caram
    11·1 answer
  • Simplify. show your work on a plz
    15·1 answer
  • Which of the following numerical expressions may represent the probability of a simple event?
    7·1 answer
  • Please help me complete the table then graph
    6·1 answer
  • Right 1, up 2<br> Rule translation
    5·1 answer
  • Marking brainliest.A block of cheese is in the shape of a triangular prism. The area of the base for the block of cheese is 96
    8·1 answer
  • An arts academy requires there to be 6 teachers for every 108 students and 3 tutors for every 36 students. students How many stu
    11·1 answer
  • Need help with this assignments
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!