Statistics and Probability Answers

a researcher thinks that if expectant mothers use vitamin pills the birth weigth of the babies will increase

There are two students who get A,B, or c grade. Find the sample space, and the values for random variable of number of students getting A grade.

A manufacturer of electronic components is interested in determining the lifetime of a certain type of battery. A sample, in hours of life, is as follows

123 116 122 110 175 126 125 111 118 117

(i) Determine the sample mean and median

(ii) What feature in this data set is responsible for the substantial difference between the two?

A finite population consists of 6 elements: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from the population.

Samples of four cards are drawn at random from a population of eight cards numbered from 1 to 6.

A. How many possible samples can be drawn?

B. Construct the sampling distribution of sample means.

1.   A population consists of the numbers 2, 4, 9, 10, and 5. Let us list all possible samples size of 3 from this population. Find the mean and variance of the sampling distribution of the sample mean.

1.   A population consisting of the values (1, 3, 5, 7). Consider all possible samples of size 2 which can be drawn with replacement from the population. Find the mean and variance of the sampling distribution of the sample mean.

In a study of the life expectancy of 450people in a certain geographic region, the mean age of death was 75 years, and the standard deviation was 5.4 years. If a sample of 45 people from this region is selected, what is the probability that the mean life expectancy will be less than 69

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 endered 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 claimof the lawyer? Use 0.05 level or significance.

The weight of 1000 children average 50 kg and the standard deviation is 5kg.

26. What is the z-score corresponds to 40 kg?