Statistics and Probability Answers

Given 𝜇=72; and 𝜎=8, find the z-score that corresponds to each of the following scores up to two decimal places. 

Identify the random sampling technique used in each item.

________________1. You are given a list of all graduating students in your school. You decide to survey every 10th student on the list and ask them the organization that they belong.

________________2. You wish to make a comparison of the gender differences in Mathematics performance. You divide the population into two groups, male and female, and randomly pick respondents from each of the group. ________________3. You assign numbers to the members of the population and then use draw lots to obtain your samples to answeryour survey on the most popular festivals in the country.

________________4. You randomly pick five out of fifteen barangays to conduct your survey in your municipality or city about their best environment-friendly practices.

________________5. You write the names of each student in pieces of paper, shuffles, and then draw eight names to answer a survey on their ethical media practices

On a final examination in mathematics, the mean was 76 and the standard deviation was 5. Determine the

standard score of a student who received a score of 88 assuming the scores are normally distributed

On a final examination in mathematics, the mean was 76 and the standard deviation was 5. Determine the

standard score of a student who received a score of 88 assuming the scores are normally distributed. (

There are 150 students in a class. The distribution if their marks in a mathematics test are as follows

Class                                                   frequency

0-9                                                      3

10-19                                                  10

20-29                                                  17

30-39                                                  x

40-49                                                  35

50-59                                                  y

60-69                                                  18

70-79                                                  10

80-89                                                  5

90-99                                                  2

Required

i)       The value of x given that the median mark is 44.357            (2marks)

ii)     The value of y given that the modal is 43.0                          (2marks)

iii)   Draw an ogive of the data in (a) above                                 (3 marks)

The probability density function for a diameter of a drilled hole in millimeters is f(x) = 10e^-10(x-5) for x > 5 mm. Although the target diameter is 5 mm, vibrations, tool wear, and other nuisances produce diameters larger than 5 mm.

a) Determine the mean and variance of the diameter of the holes. [Hint: Use integration by parts.]

b) Determine the probability that the hole exceeds 5.1 mm.

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, which is probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine:

a) the mass function of X;

b) the mean of X; and

c) the variance of X.

1000 students took an examination in Statistics and Probability. The mean score obtained is 71 and the standard deviation is 4. Assuming that the data are normally distributed, find the area and probability of students who obtained a score of:

a. at least 83

b. mean to 92

c. at most 70

Supposed that the heights of Filipino high school students are normally distributed with a mean of 158 cm and a standard deviation of 3 cm.

a. what is the area and probability of students with at least 147 cm and at most 168 cm height?

b. what is the area and probability of students with 152 cm height from the mean?

c. what are the heights of students who belong to the 80th percentile?

Suppose the mean number of days to germination of a variety of seeds is 34, with a standard deviation of 4.3 days. What is the probability that the mean germination time of a sample of 250 seeds will be within 0.5 days of the population mean?