Answer:
The 9th percentile is 40.52.
Step-by-step explanation:
We are given that the random variable X is normally distributed with a mean of 50 and a standard deviation of 7.
Let X = <u><em>the random variable</em></u>
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 50
= standard deviation = 7
So, X ~ Normal()
<u></u>
<u>Now, the 9th percentile is calculated as;</u>
P(X < x) = 0.09 {where x is the required value}
P( <
) = 0.09
P(Z < ) = 0.09
Now, in the z table the critical value of x that represents the below 9% of the area is given as -1.3543, i.e;
x = 40.52
Hence, the 9th percentile is 40.52.