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
Can someone help me ?!
True [87]

Answer:

y<-2x-3

Step-by-step explanation:

Your first step is to find the equation of the line. You can see that the y-intercept is -3, therefore your b is -3. So now your formula looks like this:

y=mx-3

To find m, you substitute in an x value and its corresponding y value. When you do this you will get -2.

Now it looks like this:

y=-2x-3.

Now that you have the equation of the line, you can look at the inequality. Since the line is dotted, that means it is not included in the inequality. That mean it cannot contain an equal to. So the only options we have are < and >. Since the shaded area is to the left, which is the negative side, we can conclude that y<-2x-3 is the correct equation.

HOPE THAT THIS IS HELPFUL!

5 0
3 years ago
Help plz right answers only if you give wrong answer or link you get reptored.
Inessa [10]

Answer:

1. The cost increases $0.30 each time 1 goldfish is

added.

7 0
3 years ago
Drag a statement or reason into the blank to complete this proof;
sergiy2304 [10]
\left[x \right] = \left[ 5\right][x]=[5]2(x+1)/−2 = 8−2 _________
_________ Simplifying

\left[x \right] = \left[ 2\right][x]=[2] = x + 1 + -4
x = -5
6 0
3 years ago
9) Gabe has a 40¢-off coupon for any kind of popcorn. He can choose
Vadim26 [7]

Answer:

Per ounce better buy is <em>Happy popcorn</em>.

Step-by-step explanation:

Given that:

Happy popcorn price for 16 ounces = $1.39

Popper popcorn price for 34 ounces = $2.79

Discount coupon present with Gabe = 40 ¢ = $0.40

To find:

Which brand is the better buy per ounce?

Solution:

First of all, let us calculate the price that Gabe has to pay after the discount coupon being applied.

Price for 16 ounces of Happy popcorn after discount = $1.29 - $0.40 = $0.99

Price for 1 ounce of Happy popcorn after discount = \frac{\$0.99}{16} = $0.062

Price for 34 ounces of Popper popcorn after discount = $2.79 - $0.40 = $2.39

Price for 1 ounce of Popper popcorn after discount = \frac{\$2.39}{34} = $0.070

Clearly, per ounce price of Happy popcorn is lesser than that of Popper popcorn.

Therefore per ounce better buy is <em>Happy popcorn</em>.

6 0
2 years ago
Help me ASAP plsssssssssssssssss
olchik [2.2K]

Answer:

4 and 9 hundreths

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Factor 5w^2-17w+65w ​2 ​​ −17w+6 completely using the box method
    10·1 answer
  • Let logb(A)=1; logb(C)=3; logb(D)=4 what is the value of logb(A^5 C^2/D^6)
    8·1 answer
  • the absolute value of a number is the distance from 0 to the number on a number line. use absolute value notation to indicate tw
    9·1 answer
  • Haley's class recycled 5 5/6 boxes of paper in a month if they recycled another 5 4/5 boxes the next month what is the total amo
    10·2 answers
  • Bailey spent $12.25 at the arcade on Saturday and $9.50 at the arcade on Sunday. How much money did Bailey spend anogether?
    15·1 answer
  • A homeowner uses GGG hours of natural gas heat and PPP hours of heat from a pellet stove to heat her house one month, with a tot
    10·1 answer
  • What is the value of 2x2 when x = 1.5?
    11·2 answers
  • 6th work. What measure of Central tendency is calculated by adding all the values and diving the sum by the number of values
    7·1 answer
  • BRAINEST TO THE CORRECT ANSWER (50 points)
    10·2 answers
  • Watch help video
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!