Answered

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 :

MrRoyal

Answer:

[tex]P(x > 4.5)= 0.983943[/tex]

Step-by-step explanation:

Given

[tex]\mu = 6[/tex]

[tex]\sigma = 0.7[/tex]

Required

[tex]P(x > 4.5)[/tex]

Start by calculating the z score

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So:

[tex]z = \frac{4.5 - 6}{0.7}[/tex]

[tex]z = \frac{-1.5}{0.7}[/tex]

[tex]z = -2.143[/tex]

So, we have:

[tex]P(x > 4.5)= 1 - P(x < 4.5)[/tex]

This gives:

[tex]P(x > 4.5)= 1 - P(x < z)[/tex]

[tex]P(x > 4.5)= 1 - P(x < -2.143)[/tex]

Using the z score probability table, we have:

[tex]P(x > 4.5)= 1 - 0.016057[/tex]

[tex]P(x > 4.5)= 0.983943[/tex]

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