A population of values has a normal distribution with \mu=239.5 and \sigma=32.7. You intend to draw a random sample of size n=139. Find the probability that a single randomly selected value is greater than 235.9. P(X > 235.9) =? Write your answers as numbers accurate to 4 decimal places.

CheemnCatelvew

CheemnCatelvew

Answered question

2020-10-18

A population of values has a normal distribution with μ=239.5 and σ=32.7. You intend to draw a random sample of size n=139.
Find the probability that a single randomly selected value is greater than 235.9.
P(X>235.9)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

izboknil3

izboknil3

Skilled2020-10-19Added 99 answers

From the provided information,
Mean (μ)=239.5
Standard deviation (σ)=32.7
Sample size (n)=139
Let X be a random variable which represents the value score.
XN(239.5,32.7)
The required probability that a single randomly selected value is greater than 235.9 can be obtained as:
P(X>235.9)=P(xμσ>235.9239.532.7)
=P(Z0.110)
=1P(Z<0.110)
=10.4562=0.5438 (Using standard normal table)
Thus, the required probability is 0.5438.

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