Statistics and Probability Answers

A store donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school.

i) What will be the probability mass function of a random variable 𝑌?

ii) What will be the expected value of 𝑌?

Three airlines serve a Srinagar. Airline 'Amira' has 50% of all the scheduled flights, airline 'Biyas' has30% and airline 'chinar' has the remaining 20%. Their on-time rates are 80%, 65%, and 40%, respectively.

Part 2) A plane has just left on time. What is the probability that it was airline 'Amira'.

The average height of students in a freshman class of a certain school has been 165.24 cm with a population standard deviation of 5.56 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 37 students in the present freshman class has an average height of 169.42 cm? Use a 0.01 level of significance.

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.

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

alex scored 90 during the first periodic exam in mathematics and 88 during the second periodic exam.The scores in first periodic exam ha a mean μ=83 and a standard deviation Ó=9.Scores in the second periodic exam ha av mean μ=8p and the standard deviation Ó=8.In which periodic exam was his standing better, assuming that the scores in his periodic exam are normally distributed?