Question

Assuming the population is normally distributed, find the probability P(x>4.5) given the mean is 6 and the standard deviation is 0.7

Answer 1

Answer:

$P(x > 4.5)= 0.983943$

Step-by-step explanation:

Given

$\mu = 6$

$\sigma = 0.7$

Required

$P(x > 4.5)$

Start by calculating the z score

$z = \frac{x - \mu}{\sigma}$

So:

$z = \frac{4.5 - 6}{0.7}$

$z = \frac{-1.5}{0.7}$

$z = -2.143$

So, we have:

$P(x > 4.5)= 1 - P(x < 4.5)$

This gives:

$P(x > 4.5)= 1 - P(x < z)$

$P(x > 4.5)= 1 - P(x < -2.143)$

Using the z score probability table, we have:

$P(x > 4.5)= 1 - 0.016057$

$P(x > 4.5)= 0.983943$