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
Novosadov [1.4K]
3 years ago
7

Question Help Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 5656 hours and a

standard deviation of 3.33.3 hours. With this​ information, answer the following questions. ​(a) What proportion of light bulbs will last more than 6262 ​hours? ​(b) What proportion of light bulbs will last 5252 hours or​ less? ​(c) What proportion of light bulbs will last between 5858 and 6262 ​hours? ​(d) What is the probability that a randomly selected light bulb lasts less than 4646 ​hours? ​(a) The proportion of light bulbs that last more than 6262 hours is
Mathematics
1 answer:
koban [17]3 years ago
5 0

Answer:

a)3.438% of the light bulbs will last more than 6262 hours.

b)11.31% of the light bulbs will last 5252 hours or less.

c) 23.655% of the light bulbs are going to last between 5858 and 6262 hours.

d) 0.12% of the light bulbs will last 4646 hours or less.

Step-by-step explanation:

Normally distributed problems can be solved by the z-score formula:

On a normaly distributed set with mean \mu and standard deviation \sigma, the z-score of a value X is given by:

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

After we find the value of Z, we look into the z-score table and find the equivalent p-value of this score. This is the probability that a score will be LOWER than the value of X.

In this problem, we have that:

The lifetimes of light bulbs are approximately normally​ distributed, with a mean of 5656 hours and a standard deviation of 333.3 hours.

So \mu = 5656, \sigma = 333.3

(a) What proportion of light bulbs will last more than 6262 ​hours?

The pvalue of the z-score of X = 6262 is the proportion of light bulbs that will last less than 6262. Subtracting 100% by this value, we find the proportion of light bulbs that will last more than 6262 hours.

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

Z = \frac{6262 - 5656}{333.3}

Z = 1.82

Z = 1.81 has a pvalue of .96562. This means that 96.562% of the light bulbs are going to last less than 6262 hours. So

P = 100% - 96.562% = 3.438% of the light bulbs will last more than 6262 hours.

​(b) What proportion of light bulbs will last 5252 hours or​ less?

This is the pvalue of the zscore of X = 5252

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

Z = \frac{5252- 5656}{333.3}

Z = -1.21

Z = -1.21 has a pvalue of .1131. This means that 11.31% of the light bulbs will last 5252 hours or less.

(c) What proportion of light bulbs will last between 5858 and 6262 ​hours?

This is the pvalue of the zscore of X = 6262 subtracted by the pvalue of the zscore X = 5858

For X = 6262, we have that Z = 1.81 with a pvalue of .96562.

For X = 5858

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

Z = \frac{5858- 5656}{333.3}

Z = 0.61

Z = 0.61 has a pvalue of .72907.

So, the proportion of light bulbs that will last between 5858 and 6262 hours is

P = .96562 - .72907 = .23655

23.655% of the light bulbs are going to last between 5858 and 6262 hours.

​(d) What is the probability that a randomly selected light bulb lasts less than 4646 ​hours?

This is the pvalue of the zscore of X = 4646

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

Z = \frac{4646- 5656}{333.3}

Z = -3.03

Z = -3.03 has a pvalue of .0012. This means that 0.12% of the light bulbs will last 4646 hours or less.

You might be interested in
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the
Vesna [10]

Answer:

A sample size of at least 1,353,733 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of .

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.  

You would like to be 98% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required?

We need a sample size of at least n.

n is found when M = 0.001.

Since we don't have an estimate for the proportion, we use the worst case scenario, that is \pi = 0.5

So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.001 = 2.327\sqrt{\frac{0.5*0.5}{n}}

0.001\sqrt{n} = 2.327*0.5

\sqrt{n} = \frac{2.327*0.5}{0.001}

(\sqrt{n})^{2} = (\frac{2.327*0.5}{0.001})^{2}

n = 1353732.25

Rounding up

A sample size of at least 1,353,733 is required.

5 0
3 years ago
Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of t
kati45 [8]

Question:

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of the numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?

Answer:

1/72

Step-by-step explanation:

<em>Morgan can roll a 17 in 3 different ways. The first way is if the first die comes up 5, the second die comes up 6, and the third die comes up 6. The second way is if the first die comes up 6, the second die comes up 5, and the third die comes up 6. The third way is if the first die comes up 6, the second die comes up 6, and the third die comes up 5. For each way, the probability of it occurring is  1/6 x 1/6 x 1/6 = 1/216. Therefore, since there are 3 different ways to roll a 17, the probability that Morgan rolls a 17 and wins the game is  1/216 + 1/216 + 1/216 = 3/216 = 1/72</em>


<em>I had this same question on my test!</em>


<em>Hope this helped! Good Luck! ~LILZ</em>


3 0
3 years ago
Please help quick!!
luda_lava [24]
C
6x^2-13X-5=0
(3X+1)(2X-5)
3x-1=0
X=1/3. 2x-5=0. X= 5/2
7 0
2 years ago
Read 2 more answers
Help please!!!!<br> Simplify the following <br> Sqrt 100 x ^13
Ket [755]

Answer:

The answer is 10x^6 * sqrt x

Step-by-step explanation:

Hope it works

3 0
3 years ago
Please help would mean a lot
jarptica [38.1K]

Answer:

1/2

Step-by-step explanation:

output devided by input

3 0
2 years ago
Other questions:
  • You are baking batches of cookies for a bake sale. Each batch takes 2.5 cups of flour. You have 18 cups of flour. Can you bake 8
    9·1 answer
  • Please Help! (only if you know what you are doing) 20 points and Brainliest
    11·1 answer
  • What is the prime factorization of 45?
    7·1 answer
  • Need a gf then i got you
    9·2 answers
  • Ayo 2+8 if u answer u get brainliest
    11·2 answers
  • Donovan can type 45 words per minute. He needs to type a report that is 9 pages long. Each page has about 300 words. What is a r
    14·1 answer
  • Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please
    11·1 answer
  • Sarah will take 8 algebra tests. On the first 7, Sarah's scores were 79, 86, 92, 89, 87, 80, and 82. What will Sarah need to sco
    6·1 answer
  • In the figure below, point O is the center of the circle and mRQ=35.
    13·1 answer
  • Miss Kito’s car holds 18 gallons of gasoline. As she was driving, she noticed that the fuel gauge indicated that she had 1/5 of
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!