The score in a certain examination follows normal distribution with mean 50 and standard deviation 16 then the marks of top 1% candidates will have score more than .................. .
87
For a normal distribution, a cut-off score x is found from the standard normal variate z: x = mean + z × standard deviation = 50 + 16z.
The top 1% of candidates lie in the upper tail with area 0.01; from the standard normal table, the z-value leaving 1% area to its right is about 2.33.
So x = 50 + 16 × 2.33 = 50 + 37.28 = 87.28, i.e. about 87 marks.
Hence, the answer is 87.
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Important Questions from Probability
- If one event is unaffected by the outcome of another event, the two events are said to be:
1. Dependent
2. Independent
3. Mutually exclusive
4. Mutually inclusive - Let $M$ be a randomly chosen non-empty subset of $S = \{1, 2, 3, \dots, 2026\}$.
Which of the following is the probability that the product of all the elements of $M$ is even? - A fair coin is tossed 6 times. The probability of getting at least 5 heads is _________________. (rounded off to two decimal places)
- Consider a random experiment of rolling a fair die. The probability of getting an odd number or a number less than 4 is ______ (Rounded off to two decimal places).
- In a null hypothesis significance test, the significance level $\alpha$ was set to 0.01. For which one or more of the following $p$ values would the null hypothesis be rejected?
