MATHEMATICS COLLEGE

The lifetime of a certain type of battery is normally distributed with mean value 11 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?

Answers

Answer 1

Answer:

Answer:

The lifetime value needed is 11.8225 hours.

Step-by-step explanation:

Problems of normally distributed samples can be 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

$Z = (X - \mu)/(\sigma)$

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 This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. This means that $\mu = 11, \sigma = 1$ .

What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?

This is the value of THE MEAN SAMPLE X when Z has a pvalue of 0.95. That is between Z = 1.64 and Z = 1.65. So we use $Z = 1.645$

Since we need the mean sample, we need to find the standard deviation of the sample, that is:

$s = (\sigma)/(√(4)) = 0.5$

So:

$Z = (X - \mu)/(s)$

$1.645 = (X - 11)/(0.5)$

$X - 11 = 0.5*1.645$

$X = 11.8225$

The lifetime value needed is 11.8225 hours.

Related Questions

Find the sum of the two polynomials (2x7−5x6−7x5+8)+(9x7−2x6−2x5−7)
The location of Sonia's school and home are plotted on the coordinateplane shown. What are the coordinates (x, y) of her school?
Find an explicit solution to the Bernoulli equation. y'-1/3 y = 1/3 xe^xln(x)y^-2
Solve the equation 2.5y +6 =4.5y -1
The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.A 2-column table with 5 rows. Column 1 is labeled x with entries 12 a m, 3 a m, 6 a m, 9 a m, 12 p m. Column 2 is labeled y with entries 6, 10, 6, 2, 6.Which equation models the data in the table? y = 6 sine (StartFraction pi Over 6 EndFraction x) + 2y = 6 sine (StartFraction pi Over 6 EndFraction x) + 4y = 4 sine (StartFraction pi Over 6 EndFraction x) + 6y = 4 sine (StartFraction pi Over 6 EndFraction x) + 10

Help please I don’t get this

Answers

Answer: 62.5 (assuming it flies straight up, because we don't know the speed of the bird going straight, left, right, or back.)

Step-by-step explanation:

They want to know how far the bird flies in a minute. What you do is you use the char to help you figure it out, by dividing the first row both by 2, so it would give the answer under the altitude column.

I need help! Please include an explanation.

Answers

Answer:

J. 144

Step-by-step explanation:

Perimeter of equilateral triangle is P = 16 + 16 + 16 = 48

Perimeter of square is P = x + x + x + x = 4x

since 4x = 48 => x = 48/4 = 12

Area of square = 12 x 12 = 144

Choose the Missing a step in the given solution to the inequality : -x- 10 > 14 +2x-x - 10 > 14 +2x
-3x - 10 > 14
————————
X< -8

Answer choices: A: -3x>24 B:-3x>4 C: -3x> -4 D: -3x<24

Answers

Answer:

A: -3x > 24

Step-by-step explanation:

The missing step above is the result of adding 10 to both sides of the inequality.

____

Comment on the solution of this inequality

The solution shown is correct and gives correct results, but it requires that you divide by a negative number. That division can be by a positive number if the first step is to add x to both sides. Then the second step is to subtract 14 and you get ...

-24 > 3x

Division by a negative number is not required, and the direction of the inequality stays the same:

-8 > x

Further comment on the solution

Using left-pointing inequality symbols (< or ≤) arranges the left-right order of the operands the same way they are arranged on the number line. That is, for the solution to this inequality, all of the values of x are to the left of -8 on the number line. Writing the inequality in the form ...

x < -8

can help you see that. A bit of mental gymnastics is required when the inequality is written ...

-8 > x

and you want to graph or choose values of x that match this result. Of course, once you have -8>x, you can easily swap sides to make it x<-8.

A: -3x>24

The working is shown

The directional derivative of f(x, y) at (2, 1) in the direction going from (2, 1) toward the point (1, 3) is −2/ √ 5, and the directional derivative at (2, 1) in the direction going from (2, 1) toward the point (5, 5) is 1. Compute fx(2, 1) and fy(2, 1

Answers

Answer:

the partial derivatives are

fx =5/9

fy =(-13/18)

Step-by-step explanation:

defining the vector v (from (2,1) to (1,3))

v=(1,3)-(2,1) = (-1,2)

the unit vector will be

v'=(-1,2)/√5 = (-1/√5,2/√5)

the directional derivative is

fv(x,y) = fx*v'x + fy*v'y = fx*(-1/√5)+fy(2/√5) =-2/√5

then defining the vector u ( from (2, 1) toward the point (5, 5) )

u=(5,5)-(2,1) = (3,4)

the unit vector will be

u'=(3,4)/5 = (3/5,4/5)

the directional derivative is

fu(x,y) = fx*ux + fy*uy = fx*(3/5)+fy(4/5)=1

thus we have the set of linear equations

-fx/√5*+2*fy/√5 =(-2/√5) → -fx + 2*fy = -2

(3/5) fx+(4/5)*fy=1 → 3* fx+4*fy = 5

subtracting the first equation twice to the second

3*fx+4*fy -(- 2fx)*-4*fy = 5 -2*(-2)

5*fx=9

fx=5/9

thus from the first equation

-fx + 2*fy = -2

fy= fx/2 -1 = 5/18 -1 = -13/18

thus we have

fx =5/9

fy =(-13/18)

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 99% confident that the sample percentage is within 5.5 percentage points of the true population percentage. Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. nequals 549 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 34% of air passengers prefer an aisle seat. nequals nothing (Round up to the nearest integer.)

Answers

Answer:

a) $n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

b) $n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{(p(1-p))/(n)})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_(\alpha/2)=-2.58, t_(1-\alpha/2)=2.58$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_(\alpha/2)\sqrt{(\hat p (1-\hat p))/(n)}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\hat p (1-\hat p))/(((ME)/(z))^2)$ (b)

We can assume that $\hat p =0.5$ since we don't know prior info. And replacing into equation (b) the values from part a we got:

$n=(0.5(1-0.5))/(((0.055)/(2.58))^2)=550.116$

And rounded up we have that n=551

Part b

$n=(0.34(1-0.34))/(((0.055)/(2.58))^2)=493.78$

And rounded up we have that n=494

Final answer:

To determine the required sample size for the survey, we can use a sample size formula based on the desired confidence level and margin of error. If nothing is known about the passenger preferences, a sample size of 549 would be needed. If a prior survey suggests a certain proportion, the sample size can be calculated using the known proportion.

Explanation:

In order to determine the number of randomly selected air passengers that must be surveyed, we need to calculate the required sample size for a desired confidence level and margin of error.

a. If nothing is known about the percentage of passengers who prefer aisle seats, we can use a sample size formula given by n = (Z^2 * p * q) / E^2, where Z is the z-score corresponding to the desired confidence level, p and q are the estimated proportions for aisle seat preference and non-aisle seat preference respectively, and E is the desired margin of error. Since a confidence level of 99% and a margin of error of 5.5% are specified, we can round up the sample size to 549.

b. If a prior survey suggests that about 34% of air passengers prefer an aisle seat, we can use the same sample size formula but with the known proportion p = 0.34. We do not have information about the non-aisle seat preference, so we cannot determine the required sample size.

Learn more about Sample size calculation here:

brainly.com/question/34288377

#SPJ11

Can some tell me how to do these

Answers

Never forget propertie of indices

Other Questions

For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03. The correlation was found to be 0.223.Select the correct slope and y-intercept for the least-squares line.a. Slope = -0.35y-intercept = -10.9b. Slope = -0.35y-intercept = 10.9c. Slope = 0.35y-intercept = -10.9d. Slope = 0.35y-intercept = 10.9

Help :,)(both questions)

Circle R has a radius of line segment of QR and QP is a tangent to circle R at point Q.(Picture attached) (a) What is the measure of RQP? Explain your answer. (b) What is the value of x? Explain your answer with work. (c) What is the measure of QRP? Explain your answer with work. (d) What is the measure of RPQ? Explain your answer with work.

About 4 out of every 5 people are right-handed. If there are 30 students in a class, how many would you expect to be right-handed? How many to be left-handed?