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

Question

asked Mar 27, 2022 85.5k views

1 Answer

MaQleod · Answer 1 · 2022-04-02T15:39:34+0000

Answer:

P(x > 4.5)= 0.983943

Explanation:

Given

$\mu = 6$

$\sigma = 0.7$

Required

P(x > 4.5)

Start by calculating the z score

$z = (x - \mu)/(\sigma)$

So:

z = (4.5 - 6)/(0.7)

z = (-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