a) The sampling distribution shape is close to normal because the number n = 40 is more than 30.

b) The sampling distribution mean x equals the population mean μ = 482 g.

c) The standard error is E = σ/√(n) = 18/√(40) = 2.85

d) P (475 ≤ x ≤ 495) = convert to standardized score

P( (475 – 482)/2.85 ≤ z ≤ (495 – 482)/2.85 ) =

P(– 2.46 ≤ z ≤ 4.56) = 0.993 use the normal distribution

e) P (x ≤ 478) = P( z ≤ (478 – 482)/2.85 ) = P( z ≤ –1.404) = 0.080

f) P (477 ≤ x ≤ 487) = P( (477 – 482)/2.85 ≤ z ≤ (487 – 482)/2.85 ) =

P(– 1.75 ≤ z ≤ 1.75) = 0.920

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