Statistics and Probability Answers

Consider the problem: According to last year's report, a Filipino household spends an average of P500 per day for food. Suppose you recently took random samples of 30 households. You determined how much each households spent for food each day and the results revealed a mean of P450 and the standard deviation of P25.50. Using a 0.05 level of significance, can it be concluded that the average amount spent per day for food of a Filipino household has decreased? Assume normality over the population

1) A package of 6 cellphones contains 4 that are slightly defective. Elise bought 4 of these CP's at random. Let the random variable be the number of non-defective CP's.

a) List the elements of the sample space using D and N for defective and non defective cell phones respectively.

b) Determine the values of the random variables and create a probability mass function.

c) Solve for the mean.

d) Solve for the variance.

e) Solve for the standard deviation.

A package of 6 cellphones contains 4 that are slightly defective. Elise bought 4 of these CP's at random. Let the random variable be the number of non-defective CP's.

a) List the elements of the sample space using D and N for defective and non defective cell phones respectively.

The mean number of minutes that android phone users spend on an app is 8.2 minutes. Suppose the standard deviation is 1 minute. Take a sample of 60 What are the mean, standard deviation for the sample mean number of app engagement by a tablet user? and Find the probability that the sample mean is between 8 and 8.5 minutes. 2.) In a recent study, the mean age of online job search website users is 34 years. Suppose the standard deviation is 15 years. Take a sample of size n=100. a.) What are the mean, and standard deviation for the sample mean ages of tablet users? Find the probability that the sample mean age is more than 30 years

A lawyer claims that the average years of settling criminal cases filed before courts is three

and a half years. To test the claim, a watchdog organization randomly selected 35 criminal

cases and recorded the years the cases took before the courts have been rendered verdicts.

The sample mean was 4 years with a standard deviation of three and a half years. Do the

data gathered by the said organization provide sufficient basis to accept the claim of the

lawyer? Use 0.05 level of significance.

A company claimed that their N95 face mask has a mean filtration efficiency rate of

95%. A group of student researcher wanted to verify this claim. They bought and tested

40 of their N95 face masks. They found out that the average filtration efficiency rate of

these face mask was 90% with a standard deviation of 4%. Test the claim at 5% level

of significance and assume that the population is approximately normally distributed.

A survey unofficially claimed that in every five young executives, only one practices good reading habits.

a. What is the probability that out of 10 young executives, two executives practice good reading habits?

b. What is the probability that at least five out of 20 young executives practice good reading habits?

the following data were obtained by sampling a population

5

3

7

5

6

8

6

5

9

Compute for the mean.

A population has mean 75 and standard deviation 12.

a.)Random samples of size 121 are taken. Find the mean and standard deviation of sampling distribution of the means?

b.)How would the answers to part (a) change if the size of the samples were 400 instead of 121?