Question

In: Statistics and Probability

Suppose x has a distribution with μ = 10 and σ = 6. (a) If a...

Suppose x has a distribution with μ = 10 and σ = 6.

(a) If a random sample of size n = 37 is drawn, find μx, σx and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)

μx =  
σx =  
P(10 ≤ x ≤ 12) =  


(b) If a random sample of size n = 59 is drawn, find μx, σx and P(10 ≤ x ≤ 12). (Round σx to two decimal places and the probability to four decimal places.)

μx =  
σx =
P(10 ≤ x ≤ 12) =

Solutions

Expert Solution

a)

Given:

= 10, = 6, n = 37

Find: P(10 < X < 12)

P(10 < X < 12) = P(0.00 < Z < 0.33)

P(10 < X < 12) = P(Z < 0.33) - P(Z < 0.00)

P(10 < X < 12) = 0.6306 - 0.5000     ...............Using standard Normal table

P(10 < X < 12) = 0.1306

b)

Given:

= 10, = 6, n = 59

Find: P(10 < X < 12)

P(10 < X < 12) = P(0.00 < Z < 0.33)

P(10 < X < 12) = P(Z < 0.33) - P(Z < 0.00)

P(10 < X < 12) = 0.6306 - 0.5000     ...............Using standard Normal table

P(10 < X < 12) = 0.1306


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