GTU 3130006 Probability and Statistics (PS) Winter 2023 Paper Solution & PDF

For a certain model car, the probability of the air conditioner failing before the warranty expires is 0.36, the probability of alternator failing is 0.26, and the probability of both failing is 0.11. Find the probability of the air conditioner or the alternator failing before the warranty expires.

A microchip company has three machines that produce the chips. Machine- I produces 45% of the chips, but 5% of its chips are defective. Machine-II produces 35% of the chips and 10% of its chips are defective. Machine-III produces the rest of the chips and 2% of its chips are defective. Find the probability of: A randomly selected chip is found to be

The following table gives the number of aircraft accidents that occurred during the various days of the week. Find whether the accidents are uniformly distributed over the week. (Use 𝜒2 at 5% level of significance for 6 degree of freedom is 12.59). Days Sun. Mon. Tue. Wed. Thu. Fri. Sat. No. of Accidents 14 16 8 12 11 9

x: 0 1 2 3 4 y: 3 6 11 18 27 Estimate the value of y when x = 5.

An insurance company has discovered that only 0.1% of the population is involved in a certain type of accident every year. If its 1000 policy-holders are selected at random from the population, what is the probability that not more than 2 of its clients are involved in such accident next year?

Suppose that the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 milliamperes and variance of 4 (milliamperes)2. What is the probability that a measurement (i) exceeds 13 milliamperes, (ii) is at most 10 milliamperes, (iii) between 10 and 13 milliamperes? [ Use: P(Z ≤ 1.5) = 0.9332].

Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in next 10 samples, (i) exactly 2, (ii) at least 4, (iii) between 2 and 7, samples contain the pollutant.

For the following data, which of the series A and B shows greater variation? Series Mean Standard Deviation A 160 10 B 60

In a partially, destroyed record on analysis of correlation data, only the following are legible: Variance of x, 𝜎𝑥 2 = 9, regression equation 8x – 10y + 66 = 0, 40x – 18y = 214. Find (i) mean values of x and y, (ii) the standard deviation of y.

1st Judge 1 6 5 10 3 2 4 9 7 8 2nd Judge 3 5 8 4 7 10 2 1 6 9 3rd Judge 6 4 9 8 1 2 3 10 5 7 Use the correlation coefficient to determine which pair of judges has the nearest approach.

To test whether a particular training improved the performance, a similar training was given to 8 participants, their scores both before and after the training are given below: Score (Before): 44 40 61 52 32 44 70 41 Score (After): 53 38 69 57 46 39 73 48 Test at 5% level of significance if the training was effective in terms of performance on the test. [Use t7,0.05 = 2.37].

A manufacturer of sprinkler systems used for fire protection in office buildings claims that the true average system-activation temperature is 130℉. A sample of size 𝑛 = 9 systems, when tested, yields a sample average activation temperature of 131.08℉. If the distribution of activation times is normal with standard deviation 1.5℉, does the data contradict the manufacturer’s claim at 1% level of significance. [Use Z0.01 = 2.58.]