For a normal curve with mean of 120 and standard deviation of 35, what proportion (in percent) of the area under the curve will lie between the values of 85 and 155 ?
68.26
Convert both limits to z-scores using z = (x - mean)/SD. For 85: z = (85 - 120)/35 = -35/35 = -1. For 155: z = (155 - 120)/35 = 35/35 = +1.
So the required area lies within one standard deviation on either side of the mean.
From the standard normal table, P(0 < Z < 1) = 0.3413, so P(-1 < Z < 1) = 2 x 0.3413 = 0.6826, i.e. 68.26 percent (the empirical 68-95-99.7 rule).
Hence, the answer is 68.26.
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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?
