Answer to Question #118629 in Statistics and Probability for Michael

Question

For a mean of 75 and a standard deviation of 3, find P(X ≥ 77 )

Answer 1

When the distribution is not mentioned, it is conventionally assumed to be Normal.

Here the distribution of X has not been mentioned, so we assume

X ~ N($\mu$ = 75, $\sigma$² = 3²)

Then by the property of Normal distribution,

Z = $\frac{x-\mu}{\sigma}$ ~ N(0, 1) i.e. Z is a standard normal variable

Therefore, P(X $\geq$ 77)

= P($\frac{x-75}{3}\geq\frac{77-75}{3}$)

= P(Z $\geq$ 0.67)

=1 - P(Z < 0.67)

= 1 - $\Phi$(0.67)

= 1 - 0.7486 = 0.2514 [using standard normal distribution table]

Answer: The value of P(X ≥ 77) is 0.2514.