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
fomenos
3 years ago
9

The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There

are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?
Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
4 0

Answer:

z=1.64

And if we solve for a we got;

10 +1.64*1=11.64

So the value of height that separates the bottom 95% of data from the top 5% is 11.64  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent certain lifetime of a population, and for this case we know the distribution for X is given by:

X \sim N(10,1)  

Where \mu=10 and \sigma=1

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.05   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.64

And if we solve for a we got;

10 +1.64*1=11.64

So the value of height that separates the bottom 95% of data from the top 5% is 11.64  

You might be interested in
A restaurant employs five people. The two cooks
shusha [124]

Answer:

Step-by-step explanation:

explain the question pls so I can help

6 0
2 years ago
A line with a slope of 3 passes through the point (0, -10). What is its equation in
andrey2020 [161]

(\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{3}(x-\stackrel{x_1}{0}) \\\\\\ y+10=3x\implies \stackrel{\textit{slope-intercept form}}{y=3x-10}

8 0
2 years ago
Determine if you’re finding the part percent or whole 12 is 50% of what number
bearhunter [10]

Answer:

whole

Step-by-step explanation:

8 0
3 years ago
Find x on this special right triangle
tigry1 [53]

Answer:

The answer is 7

Step-by-step explanation:

We know than Tan45=1

Tanx=opp/adj

tan45=y/(7\sqrt{2})/2

Thus y=7\sqrt{2}/2

We know by pythagoras theorem that hyp^2=side^2+side^2

x^{2}=((7\sqrt{2} /2)^{2}+(7\sqrt{2}/2)^{2}

x^{2}=(49(2)/4)+(49(2)/4)

x^{2}=(49/2)+(49/2)

x^{2}=(98/2)

x^{2}=49

x=7

6 0
2 years ago
40 POINTS GIVEN PLEADE ANYONE HELP I NEED IT ASAP MY SESSION WILL EXPIRE
Juli2301 [7.4K]
Will put 8 ounce in the. up because first you subtract the 16 ounces the he used to fill his bottle which leaves you with 128 ounces and you will divide the 128 by the 16 cups to get x equals 8 ounces.
8 0
3 years ago
Read 2 more answers
Other questions:
  • in a candy store a $5 jar of candy is labeled 50% off what is the discount what is the sale price of the jar of candy
    10·1 answer
  • A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed
    14·1 answer
  • A photographer has 591 photos of animals and 234 photos of plants. He wants to put all of the photos into photo books. Each page
    10·2 answers
  • Select all of the situations below that can be modeled by the expression 4 + 3x.
    13·1 answer
  • The six-digit number 63X904 is an even multiple of 27. What does the digit X represent?
    11·1 answer
  • 0.7 , 2/3 , 5/8 , 65% in least to greatest
    10·2 answers
  • 10^-2 + 8 round the coefficient to two decimal places​
    7·2 answers
  • A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find cos B, tanB, and sin B. (Plz I need he
    11·1 answer
  • What is the product of (2p + 7)(3p2 + 4p – 3)?
    14·1 answer
  • Available is 23 cm taller than Olivia is half the height of Luca. If lucas is 1.77m tall, how tall are available and Olivia? Exp
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!