Question

Find the probability of being below 514 if the mean of a normal distribution is 474 and the standard deviation is 32.

Question 13 options:

.8461


.8944


.1056


.1539

Answer 1

I think it is c not sure tho

Answer 2

Second option is correct. That is the probability of being below 514 with the mean  474  and standard deviation 32 is 0.8944.

What is normal distribution?

A function that represents the distribution of many random variables as a symmetrical bell shaped graph.

The normal distribution is a probability distribution, so the total area under the curve is always 1 or 100%.

What is z-score?

A z-score is a numerical measurement that describes a value's relationship to mean of a group of values.

Formula for calculating z-score

z = (x -μ)/σ

where,

z is standard score

x is observed value

μ is mean of sample

σ is standard deviation of sample

According to the given question

we have

x = 514

μ = 474

and

σ =32

therefore,

Z- score will be

Z = (514 -474)/32 = 1.25

So, the area under the normal distribution curve z<1.25

⇒ P(x<1.25) = P(Z<1.25) = 0.894

Hence, second option is correct one. That is, the probability of being below 514 if the mean of a normal distribution is 474and the standard deviation is 32 is 0.894.

Learn more about the probability under normal distribution here:https://brainly.com/question/15103234

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