Math Answers

Translate the following into symbolic

form and give its domain.

1. All fishes are swimmers.

2. Some fruits are sweet.

3. Every number is a real number.

4. Any mammal is not two-legged.

1. A population of 4 numbers 1,2,4,5

a. List ALL the possible samples of size n=3, which can be drawn with replacement from the population.

b. Construct a sampling distribution of the sample mean.

1. A population consists of 4 numbers 3,7,11,15 of sample size n=2 which can be drawn without replacement from the population.

a. Population mean

b. Population Variance

c. Population standard deviation

d. Mean of the sampling distribution of the sample means

e. Variance of the sampling distribution of the sample means

f. Standard deviation of the sampling distribution of the sample means

Evaluate:

sin 30⁰ cos 45⁰ − cos 30 ⁰ sin 45⁰

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?

Determine the volume of the solid generated when the region bounded by the curve y^2=x^3 and the x-axis, is revolved about the line y=2

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].

a. for the top and bottom of the box costs P30 per square centimeter and the material for the sides cost P15 per square centimeter. Find the dimensions of the box so that the total cost of material is the least possible and all its dimensions do not exceed 20cm.

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