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A population of values has a normal distribution with μ=26μ=26 and σ=31.6σ=31.6. You intend to draw...

A population of values has a normal distribution with μ=26μ=26 and σ=31.6σ=31.6. You intend to draw a random sample of size n=214n=214.

Find the probability that a single randomly selected value is between 21.5 and 22.5.
P(21.5 < X < 22.5) =

Find the probability that a sample of size n=214n=214 is randomly selected with a mean between 21.5 and 22.5.
P(21.5 < M < 22.5) =

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A population of values has a normal distribution with μ-26 and σ 31 .6 Sample size (n)-214 The probability that a single randomly selected value is between 21.5 and 22.5 P(21.5 < X < 22.5) = P(215-μ < x-u < 22.5-μ) 1.5-26 22.5-26 31.6 31.6 = P(-0.1 424c Z<-0.1 1 08) = P (-0.1424 < Z < 0)-P (-0.1 108-Z-0) 0.0557-0.0438[From standard Normal table] =0.0119 P(21.5<X<22.5) The probability that a sample ofsize n-214 is randomly selected with a mean between 21.5 and 22.5 21.5-u M-u 22.5-u PC2 1.5 < M < 22.5)=P(-ㄧㄑㄒㄑㄧ -) Vn 21.5-μ vn 21.5-26 1.6 214 vn < 22.5-26 ( = P(-2.0832< Z<-1.6203) = P (-2.0832 < Z < 0)-P (-1.6203-Z < 0) = 0.0338 21.6 V214 =0.4812-0.4474 [From standard Normal table] P(21.5<M< 22.5)

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