Question

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

Answer 1

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.

`z=(x-\mu)/(\sigma)`, where,

z = z-score,

x = Random sample score,

`\mu` = Mean,

`\sigma` = 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
`1.96`.

`1.96=(x-186.4)/(48.9)`

Let us solve for x.

`1.96\cdot 48.9=(x-186.4)/(48.9)\cdot 48.9`

`95.844=x-186.4`

`95.844+186.4=x-186.4+186.4`

`282.244=x`

Therefore, the range
`x>282.244` represents the upper 2.5% of the data.