Question

Determine the following if X ~ N(153 ; 25): P(X > 160)

Answer 1

To find P(X > 160), we first need to standardize the normal distribution with mean 153 and variance 25.

Z = (X - mean) / standard deviation
Z = (160 - 153) / √25
Z = 7 / 5
Z = 1.4

Now, we can look up the probability of Z = 1.4 in a standard normal distribution table or use a calculator to find P(X > 160) = P(Z > 1.4).

Using a standard normal distribution table or calculator, P(Z > 1.4) is approximately 0.0808.

Therefore, P(X > 160) is approximately 0.0808 or 8.08%.