HSC Commerce कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company takes at most 500 days to complete the flyover?

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Normal distribution was invented by

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If X ~ N(9, 81) the standard normal variate Z will be

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If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is

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If X ~ N(µ, σ²), the maximum probability at the point of inflexion of normal distribution

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In a parametric distribution the mean is equal to variance is

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In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

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The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`

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A manufacturer produces switches and experiences that 2 percent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :

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An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is

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If for a binomial distribution b(n, p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to

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The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are

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Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?

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Which of the following statements is/are true regarding the normal distribution curve?

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Which of the following cannot generate a Poisson distribution?

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The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

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The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?

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In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?

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A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

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Cape town is estimated to have 21% of homes whose owners subscribe to the satellite service, DSTV. If a random sample of your home is taken, what is the probability that all four homes subscribe to DSTV?