Solve for x. −12 = − 3/4 x A) 6 B) 8 C) 12 D) 16

The lifetime of a cheap light bulb is an exponential random variable with mean 36 hours. Suppose that 16 light bulbs are tested

photoshop1234 [79]

Answer:

$P(T$

Step-by-step explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}, x>0$

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

$X \sim Exp(\lambda=\frac{1}{16})$

Or equivalently:

$X \sim Exp(\mu=16)$

Solution to the problem

For this case we are interested in the total T, and we can find the mean and deviation for this like this:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}=\frac{T}{n}$

If we solve for T we got:

$T= n\bar X$

And the expected value is given by:

$E(T) = n E(\bar X)= n \mu= 16*36=576$

And we can find the variance like this:

$Var(T) = Var(n\bar X)=n^2 Var(\bar X)= n^2 *\frac{\sigma^2}{n}=n \sigma^2$

And then the deviation is given by:

$Sd(T)= \sqrt{n} \sigma=\sqrt{16} *36=144$

And the distribution for the total is:

$T\sim N(n\mu, \sqrt{n}\sigma)$

And we want to find this probability:

$P(T< 600)$

And we can use the z score formula given by:

$z=\frac{T- \mu_T}{\sigma_T}$

And replacing we got this:

$P(T$

6 0

2 years ago

Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases. (Assume that centra

Triss [41]

Answer:

Step-by-step explanation:

a) this involves 2 tails

The critical value is determined from the t distribution table.

α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Looking at 0.975 with df 10

The critical value is 2.228

b) α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Looking at 0.975 with df 20

The critical value is 2.086

c) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Looking at 0.995 with df 20

The critical value is 2.845

d) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Looking at 0.995 with df 60

The critical value is 2.660

e) 1 - α = 1 - 0.01 = 0.99

Looking at 0.99 with df 10

The critical value is 2.764

f) 1 - α = 1 - 0.025 = 0.975

Looking at 0.975 with df 5

The critical value is 2.571

6 0

1 year ago

All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that rep

prohojiy [21]

So the original price is "x".

the discounted price by 10% is P(x) = 0.9x.

the price minus a $150 coupon is C(x) = x - 150.

so, if you go to the store, the item is discounted by 10%, so you're really only getting out of your pocket 90% of that, or 0.9x, but!!! wait a minute!! you have a $150 coupon, and you can use that for the purchase, so you're really only getting out of your pocket 0.9x - 150, namely the discounted by 10% and then the saving from the coupon.

C( P(x) ) = P(x) - 150

C( P(x) ) = 0.9x - 150

5 0

2 years ago

Read 2 more answers

Kelly wants to know the actual value of a house that she wants to buy. What should she do?

Ghella [55]

Kelly should ask the realtor.

5 0

1 year ago

Read 2 more answers

6x+7y=4x+4y6x+7y=4x+4y6, x, plus, 7, y, equals, 4, x, plus, 4, y Complete the missing value in the solution to the equation. ((l

tia_tia [17]

Answer: