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let x be a normally distributed random variable with mean 5 and standard deviation 15. please express your answer as a number between 0 and 100. if you want to write 52%, please enter 52. what is the probability that x is less than or equal to 28?

Answer :

As per the normal distribution, the probability that x is less than or equal to 38 is 0.9861.

Probability:

In math, probability denotes a  branch of mathematics concerning numerical descriptions of how likely an event is to occur.

Given,

Here let x be a normally distributed random variable with mean 5 and standard deviation 15. please express your answer as a number between 0 and 100. if you want to write 52%, please enter 52.

Here we need to find the probability that x is less than or equal to 28.

According to a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

Here first, we have to solve for the z-score using the formula below.

=> z-score = (x – μ) / σ

Here x refers the individual data value = 38

μ refers mean = 5

σ refers standard deviation = 15

Then when we apply the values on it, then we get,

=> z-score = (38 - 5) / 15

=> z-score = 33 / 15

=> z-score = 2.2

Then the probability that corresponds to the z-score in the z-table.

=> probability = 0.9861

To know more about Probability here.

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