Answer:
44.85.
Step-by-step explanation:
We have been given that the random variable X is normally distributed, with mean u=50 and standard deviation SD=6. We are asked to find the 15th percentile.
We will use normal distribution table to find the z-score corresponding to 15th percentile or 0.15.
Using normal distribution table, we will get z-score of [tex]-1.03[/tex].
Now, we will use z-score formula to find corresponding x-value to z-score of [tex]-1.03[/tex].
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = Z-score,
x = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values, we will get:
[tex]-1.03=\frac{x-50}{6}[/tex]
[tex]-1.03*5=\frac{x-50}{6}*6[/tex]
[tex]-5.15=x-50[/tex]
[tex]-5.15+50=x-50+50[/tex]
[tex]44.85=x[/tex]
Therefore, the 15th percentile is 44.85.
