Question

X is a normally distributed random variable with a mean of 100 and a variance of 144. Use Excel to find the value of X that gives a probability of 10% on the right. In other words, find Xo such that P(X > Xo) = 0.10. Write your answer to 4 decimal places.

• A.

  115.3672

• B.

  115.3786

• C.

  115.3600

• D.

  115.3721

Answer 1

correct option B. 115.3786

Given,

mean = 100

variance = ² = 144

So,

standard deviation = = 12

Now, Using standard normal table,

P(Z > z) = 10%

=> 1 - P(Z < z) = 0.1

=> P(Z < z) = 1 - 0.1 = 0.9

=> P(Z < 1.2816) = 0.9

z = 1.2816

Therefore,

Using z-score formula,

X₀ = z * +

X₀​  = 1.2816 * 12 + 100 = 115.3792

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