Consider a normal distribution of values with a mean of 32 and a standard deviation of 1.5. Find the probability that a value is less than 36.8. Anyone know?

Question

asked Dec 22, 2022 73.2k views

1 Answer

Fiehra · Answer 1 · 2022-12-29T07:41:23+0000

Answer: The probability that a value is less than 36.8 is 0.9993.

Explanation:

Let X be the random variable that normally distributed.

Given:
$\mu=32,\sigma=1.5$

The probability that a value is less than 36.8 =
P(X<36.8)

$=P((X-\mu)/(\sigma)<(36.8-32)/(1.5))\\\\=P(Z<3.2)\ \ \ [Z=(X-\mu)/(\sigma)]\\\\=0.9993$ [Using P-value calculator]

Therefore, The probability that a value is less than 36.8 is 0.9993.