Statistics and Probability Answers

From the area planted in one variety of guayule, 25 plants were selected at random. Of these plants, 13 were “ Off types” and 12 were “Aberrant” The rubber
percentages of these plants were:

Off types 4.47 5.88 6.21 5.55 6.09 5.70 5.82 4.84 5.59 5.59 5.22 4.45 6.76
Aberrant 6.48 6.36 4.28 7.71 6.40 7.06 5.51 8.93 7.71 7.20 7.37 5.91

Compute a 90% confidence interval for the difference of two population means. Also interpret your results. Also test the hypothesis that two types of plants have equal average rubber production.

The two samples A and B detailed below were taken from normal population of standard deviation 2.5.

A 16 18 23 26 19 24 25 23 21 22 20
B 20 21 23 25 27 24 26 24 28 20 30
Compute a 90% confidence interval for real difference and decide whether the difference of sample means is significant (that the population means are different or same). Also test the hypothsis that the two populations have equal means.

Q.1
a. Find a 90% confidence interval for the mean of normal distribution if σ =3 and if a sample of size 10 gave the values 9, 14, 10, 12, 7, 13, 11, 12, 15, 12. What would be the confidence interval if σ is unknown?
b. The breaking strength of 10 specimens of 0.104 inches diameter hard drawn copper wire are found to be 578, 572, 570, 568, 572, 570, 570, 572, 596, 584 pounds. Calculate the 95% confidence interval for the mean breaking strength of this kind of wire, assuming that the measurements are normally distributed. Also test the hypothesis that the average breaking strength of this type of wire is 590.

The manager of a bottling plant is anxious to control the mean net weight of fruit bottled. Over a long period, the variance has been 45.2 gm. A new machine is introduced and the net weights (in grams) in randomly selected bottles (all of the same nominal weight) are 987, 966, 955, 977, 981, 967, 975, 980, 953, 972. Would you report to the manager that the new machine has a mean net weight of fruit equal to 975 grams? Also calculate 95% confidence interval for the variance.

Two cards are draw at random from a well shuffled pack of 52cards. Find the probability that:
• Both are the same color
• Both are the different color

An experiment involves studying the composition of genders of a set of triplets What is the probability that there are 2 boys and a girl in the set?

a. 0.875
b. 0.125
c. 0.375
d. 0.625

If a random variable X follows Normal distribution such that P (9.65<=X<=13.8)=0.07008and P(X>9.6)=0.8159 where Find the mean & variance of X and find P(X>=13.8 /X>=9.6).