Statistics and Probability Answers

The salary of workers of an industry is normally distributed with mean salary of 420 Birr and standard deviation of 55 Birr. If any one worker from the industry is selected randomly,
i) What is the probability that he or she has salary of
a) More than 450 Birr
b) Less than 300 Birr
c) Between 380 and 490 Birr
ii) What is the salary
a) Below which 5% of workers have it
b) Above which 35% of workers have it

7. Two random samples drawn from two normal populations are
Sample I 20 16 26 27 23 22 18 24 25 19 - -
Sample II 27 33 42 35 32 34 38 28 41 43 30 37
Obtain the estimates of the variances of the population.

i would like to ask the answer in this prob.
3.A statistics instructor at a large western university would like to examine the link (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of the number of these problems completed during the course of the semester. At the end of the class each student’s ttal is recorded along with their final grade. Test statistic = 0.885 with α = 0.05; df = 10; tcrit = ± 2.228 and tcalc = 6.0.

The rate of defectiveness of items from a production line is 2% five items are randomly selected from the production line
a) present the probability distribution table .
b) At least two items are defective
c) At least two items are defective
d) Given that 100 items we're randomly selected instead, find the average number of defective items

1. Researchers asked a group of adolescents aged 3-15 the following question: “On a scale of 0-3, with
0 being the worst and 3 being the best, how much do you like unicorn giggles?” Their responses are
stratified by age group in the table below.
“0” “1” “2” “3”
3-7 years old 5 2 15 23
8-12 years old 20 15 2 14
13-15 years old 2 0 5 29
Test whether their responses are independent of age group at the α = 0.05 level of significance.
(a) State the null and alternative hypotheses, and use StatCrunch to calculate the P-value. Write
down the steps you take in StatCrunch as well as any statistics for which StatCrunch prompts
you.
(b) State your decision (with appropriate reasoning), and write a thorough conclusion

Two soil samples consisting of 21 and 9 observations have variances of 18 and 8 respectively. Test the hypothesis that the first population variance is greater than the second at (a) 0.05 and (b) 0.01 levels of significance. (c) Repeat the same test If the two samples consist of 60 and 120 observations.

The loss due to an earthquake in a commercial building is modelled by a random variable X with density function f(x) =0.005(20−x), for 0 < x < 20 0, elsewhere Given that the fire loss exceeds 10, what is the probability that it exceeds 18

Let X be a continuous r.v with density function f(x) =(|x| 10 , for −2 < x < 4 0, elsewhere
. Calculate the expected value of X.

Suppose that 3% of computer chips produced by a certain machine are defective. The chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective chips?