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X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let...

X ~ N(70, 14). Suppose that you form random samples of 25 from this distribution. Let X bar be the random variable of averages. Let ΣX be the random variable of sums. Find the 40th percentile

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Expert Solution

Given that,

mean = = 70

standard deviation = = 14=3.7417

n = 25

= 70

= / n = 3.7417 /25=0.74834

Using standard normal table,

P(Z < z) =40%

= P(Z < z) = 0.40  

= P(Z < -0.25) = 0.40

z = -0.25

Using z-score formula  

= z * +

= -0.25*0.74834+70

= 69.8129

answer =70

milcah answered 1 month ago
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