Math Answers

An electrical firm produces light bulbs that have a length of life that is approximately normally distributed with a mean of 650 hours and a population standard deviation of 20 hours. A new version of light bulbs is being produced and is assumed to be better than the previous version. To test this claim, a random sample of 52 new light bulbs are tested. Would you agree with this claim if the random sample showed an average of 760 hours? Use a 0.01 level of significance.

It is claimed that a car is driven on the average less than 28700 kilometers per year with a population standard deviation of 2100 kilometers. To test this claim, a random sample of 58 car owners are asked to keep a record of the kilometers they travelled. Would you agree with this claim if the random sample showed an average of 22500 kilometers? Use a 0.01 level of significance

The average height of students in a freshman class of a certain school has been 161.27 cm with a population standard deviation of 6.5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 45 students in the present freshman class has an average height of 150.6 cm? Use a 0.05 level of significance.

(i)Find the volume of the solid that is generated by revolving the region bound by the

graphs of 𝑦 = 𝑥2 and 𝑦2 = 𝑥 about the 𝑦 − 𝑎𝑥𝑖𝑠.

Find the expected value of the random variable X and its variance having the following density function:

f(x) = 5 (1-x4) 0<x<2

= 0 elsewhere

Full details math and explain.

1. A six pumpkins are displayed in a store a population consists of 6 values (19,14,15,9,10. and 17). Suppose that random sample size 2 are taken form this population

a. How many samples are possible? List them and compute the mean of each sample

b. Construct the sampling distribution of the sample means

c. Construct the histogram of the sampling distribution of the sample means

1. A six pumpkins are displayed in a store a population consists of 6 values (19,14,15,9,10. and 17). Suppose that random sample size 2 are taken form this population

a. How many samples are possible? List them and compute the mean of each sample

b. Construct the sampling distribution of the sample means

c. Construct the histogram of the sampling distribution of the sample means

What percentage of $320.80 is $111.28

$500 is deposited in an account which bears 12%p.a interest compound monthly. Use the compound interest formula to find the number of years it would take to accumulate $500 to $806.11

Find the asymptotes of the curve 𝑥2𝑦 − 𝑥𝑦2 + 𝑥𝑦 + 𝑦2 + 𝑥 − 𝑦 = 0.