If the random variable X is normally distributed with mean 80 and standard deviation
5, then find (i) P[60.5 < X < 90], and (ii) P[X _ 80 < 1].
To solve this problem using statistical techniques, you can apply the properties of the normal distribution. For a random variable X that is normally distributed with a mean (μ) of 80 and a standard deviation (σ) of 5, we can use the standard normal distribution (z-distribution) to calculate probabilities. Here's how you can find
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Calculate the 5-yearly moving average for the following data of the profits of a
company (in Rs. Lakhs) during 1995 to 2010:
.
An insurance company insured 1000 scooter drivers, 3000 car drivers and 6000 truck
drivers. The probabilities that the scooter, car and truck drivers meet with an
accident, are 0.02, 0.04 and 0.25, respectively. One of the insured driver meets with
an accident. What is the probability that he is a (i) car driver; (ii) truck driver?
State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.
A company appointed four salesman A, B, C and D and observed their sales in three
seasons – Summer, Winter and Monsoon. Test whether the average sales of the four
salesmen differ in amount (in Rs. Lakhs) as given below by one-way analysis of
variance (ANOVA) using observations after taking deviation from 30.
The monthly income (in Rs. Lakhs) of five employees in a company are as follows:
25, 20, 30, 15, 10. (i) List all possible samples (without replacement) of size 2 (ii)
Compute the mean of all samples and set up the sampling distribution of sample
mean.
Write three advantages and three limitations of systematic sampling
In a partially destroyed laboratory record of an analysis of correlation data, the
following results are legible:
The equations of two regression lines are as follows:
3Y 9X 46
3X 12Y 19
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 
Obtain (i) mean values of X and Y; (ii) the values of regression coefficients; and (iii)
the value of correlation coefficient.