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.

Step-by-step 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 = $P(X<36.8)$

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

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