Statistics and Probability Answers

A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life of the batteries in hours until failure is:  342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, 298 . What would you advise if the manufacturer wanted to say in advertisement that these batteries last more than 400 hours?

Let (X,Y) be a two-dimensional continuous random variable with joint P.d.f

𝑓𝑋𝑌

(𝑥,𝑦) = {

2 , 0 < 𝑥 < 𝑦 < 1

0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Find the marginal distribution for X and Y ?

Consider independent random variables Zi ∼ N(0, 1), i = 1, …, 16, and let Z be the sample mean. Find:

a) P[Zbar <1/ 2].

b) P[Z₁ − Z₂ < 2].

c)P[Z1 + Z2 <2].

on a recent math test , the mean score was 75 and the standard deviation was 5. mike got 85. what percentile does he fall in?

a line up for tickets to a local concert had an average waiting time of 20 minutes with a standard deviation of 4 minutes

a. what percentage of the people in line waited for more then 20 minutes

A random of 25 sample is drawn from a population with sample mean 105.2 and standard deviation 11.13 Construct a 90% confidence interval. *

Provide step-by-step solutions to the given problem below. Write your answers on

the spaces provided.

Consider all samples of size 2 from the population 2, 5, 6, 9, 11, and 13. Compute

the mean, and variance of the sampling distribution of the sample mean.

First step:

Second step

a)

b)

Third step

Fourth step

Fifth step

Sixth step

a)

b)

Seventh step

a)

b)

c)

d)

If the sample mean is 75 and the sample standard deviation is 5.Find the corresponding standard deviation of the score 70

Use formula to find z score z=x–x/ó

Use the Standard normal Curve to answer the following,On the first periodic exam in statistics,the population mean was 70 and the standard deviation was 9.Determine the standard score of the student who got a score of 88 assuming the score was normally distributed.

Consider a population which is normally distributed.If the variance of the population is 9 and n=9,what is the variance of the sampling distribution of sample means