Question

The mean of a normal distribution is 50 and 5% of the values are
greater than 60. Find the standard deviation of this distribution.
(Given the area under standard normal curve between z = 0 and
z = 1.64 is 0.45)​

Answer 1

Answer:

μ = 50q

We need to find σ.

Let X be a random variable having normal distribution.

It is given that 5% of the values are greater than 60. This means P(X > 60) = 0.05. Which means P(X ≤ 60) = 1 - P(X > 60) = 1 - 0.05 = 0.95

If we normalise X, then it will become z = (X-μ)/σ.

We need to find value of z, such that P(z) = 0.95

We can use a table of normal distribution and values. By doing so, we find that z = 1.645

z = (X-μ)/σ.

Hence σ = (X-μ)/z = (60–50)/1.645 = 10/1.645 ≈ 6.079

Step-by-step explanation:

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