Statistics and Probability Answers

Eleven school boys were given a test in Drawing. They were given one
month's further tuition and a second test of equal difficulty was held at the end
of it. Do the marks give evidence that the students have benefited by the extra
coaching? Use α=0.05.
Roll
No
1 2 3 4 5 6 7 8 9 10 11
Marks
T1
28 20 19 21 18 20 18 17 23 16 19
Marks
T2
20 19 22 18 20 22 20 20 20 20 17
(b) The nine items of sample had the following values. 45, 47, 50, 52, 48, 47, 49,
53, 51. Does the mean of nine items differs significantly from an assumed
population mean of 47.5

You have to examine the relationship between the age and price for used cars
sold in the last year by a car dealership company. Fit a simple linear regression
model Price Sold on Car age.
(b) Find the estimated linear regression values of Y.
(c) Show that the sum of Deviations of estimated values from actual values is
zero.
(d) Show that the sum of squares of residuals is minimum.
(e) Find the standard error of estimate. Calculate the Correlation Co-efficient y on x.
(g) Find the Co-efficient of Determination.
Car Age (in years) Price (in dollars)
4 6300
4 5800
5 5700
5 4500
7 4500
7 4200
8 4100
9 3100
10 2100
11 2500
12 2200

What is the probability that the total of two dice will be greater than 8, given
that the first die is a 6?

Let A denote the event 'student is female' and let B denote the event 'student is
French'. In a class of 100 students suppose 60 are French, and suppose
that 10 of the French students are females. Find the probability that if I pick a
French student, it will be a girl that is, find P (A|B).

Draw all possible random samples of size 2 with replacement from the
population 2, 3, 4, 5 and 7. Similarly draw all possible random samples of size
2 with replacement from other population 1, 2, 2, 4 and 5.Find the sampling
distribution of difference b/w two sample means and calculate its Mean,
Variance and Standard Error. Also find the Mean, Variance and Standard
Deviation of two Populations and Verify the Results.

A manufacturer uses electrical fuses in an electronic system. The fuses are purchased in large lots and tested sequentially until the first defective is observed. If the lot contains 10% defective fuses, find the probability that 5 fuses are tested before a defective fuse is observed.

twin city the probability that a power engine from CDA (Capital development Authority) is available when needed is 0.45 and the probability that a power engine from RDA (Rawalpindi development Authority) is available when needed is 0.45. What is the probability that the engines neither from CDA nor from RDA are available when needed?

A six sided die is rolled 12 times. What is the probability of getting a 4 five times

Estimate the rainfall (inches) corresponding to the seeds per acre 12 kg and the temperature 38°C from the following results- Trait SD 28.02 gm 4.42 0.80 4.91 inch 1.10 85 Mean 712 -0.56 36°C -0.40 where X is (kg) per acre, Xg=Ratanlal (inches), X, temperature (C}.