Question

A normal distribution has a mean of 10 and a standard deviation of 1. What is the probability of selecting a number that is at most 10? Leave the answer in decimal form to 3 decimal places.​

Answer 1

Answer: 0.500

Explanation:

Given : A normal distribution has a mean
`(\mu)` of 10 and a standard deviation
`(\sigma)` of 1.

Let x be a random variable that represents numbers .

The probability of selecting a number that is at most 10 will be

`P(x\leq10)=P((x-\mu)/(\sigma)\leq(10-10)/(1))\\\\=P(z\leq0)=0.500`

As the area occupied by standard normal curve less than equal to 0 = 0.500

So, required probability = 0.500