Question

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?

Answer 1

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.