A normal distribution has a mean of 186.4 and a standard deviation of 48.9.

What range of values represents the upper 2.5% of the data?

a

X > 235.3

b

X > 333.1

c

X > 284.2

d

X > 186.4

We have been given that a normal distribution has a mean of 186.4 and a standard deviation of 48.9. We are asked to find the range of value that represents the upper 2.5% of the data.

We know that upper 2.5% of data would be 97.5% of data.

We will use z-score formula to solve our given problem.  

, where,

z = z-score,

x = Random sample score,

= Mean,

= Standard deviation.

Now we will use normal distribution table to find z-score corresponding to 97.5% area or 0.975.

We can see from the normal distribution table that z-score corresponding to  area 0.975 is .

Let us solve for x.

Therefore, the range represents the upper 2.5% of the data.

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