Statistics and Probability Answers

Aina and Joan invest in each account.Aina invests Php 275,000 at 10% for 15 years and joan invests Php 275,000 at 12% for 12 years.Both investments are compounded annually.Which one will yield more?

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Perform Hypothesis Testing

1. A factory manufacturing light-emitting diode (LED) bulbs claims that their light bulbs last for 50,000 hours on the average. To confirm if this claim is valid, a quality control manager got a sample of 50 LED bulbs and obtained a mean lifespan of 40,000 hours. The standard deviation of the manufacturing process is 1000 hours. Do you think that the claim of the manufacturer is valid at the 5% level of significance?
2. A presidential candidate asks a polling organization to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. Out of 2500 respondents in the sample, 925 said they would vote for him. If 40% of the potential voters vote for his rival, is this significantly different from the percentage of potential voters of the candidate who requested the survey? Use 5% level of significance.

Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 98.65 degrees and a standard deviation of 0.8 degrees. If 50 healthy people are selected at random, what is the probability that the average temperature for these people is 98.45 degrees or higher?

 From a box of a dozen rocket-propelled grenade (RPG), 4 are selected at random and fired. If the box contains 3 defective RPG’s, what is the probability that (a) all 4 will fire? (b) at most 2 will not fire? 

If the population consists of numbers 1, 2 ,3, 4, 5 and 6, find the mean of the samples of size of 3. Construct a sampling distribution and make a histogram for the sample distribution.

The mean and the standard deviation of the breaking strength of 100 cables tested by the company is 180 lbs and 25 lbs . Find 95% confidence limit of breaking strength of all cables manufactured by the company

Ans: (180- 24.9 , 180+24.9)

 A presidential candidate asks a polling organization to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. Out of 2500 respondents in the sample, 925 said they would vote for him. If 40% of the potential voters vote for his rival, is this significantly different from the percentage of potential voters of the candidate who requested the survey? Use 5% level of significance.

D. Determine the possible values and construct the probability distribution for the random

variables described in each of the following situations. Draw the corresponding histogram for each

probability.

1. Two balls are drawn in succession without replacement from an urn containing 5 red balls and

6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability distribution of the random variable Z.

Possible Outcome

Value of the Random

Variable Z

Value of the Random

Variable z

Probability P(Z)

Determine the possible values and construct the probability distribution for the random variables described in each of the following situations. Draw the corresponding histogram for aech probabilty

2. A shipment of five computers contain two that are defective. If a reatailer receives three of these compiters at random, list the elements of the sample space S using the letters D and N for defective and non-defective computers, respectively. To each sample point assign a value x of the random variable x representing the number of computers purchased by the retailer which are defective.

 If x has the probability function 𝑓(𝑥) = 𝑘/2^x for x=0,1,2,……… then determine the followings

a) Vale of k

b) P(x≥ 4)