PrtSc 3. Anand m sample of n= 100 observations is selected from a population wit

Question

PrtSc 3. Anand m sample of n= 100 observations is selected from a population with-30 and =22. Complete parts ath 1 Click the icon to view the table of normal curve areas. a·Find , and 8a-30 (Round to one decimal place as needed.) b. Describe the shape of the sampling distribution of x. Inform A. Uniform distribution 0 B. Skewed left nvSD C. Approximately normal O D. Skewed right c. Find P(x 2 28). P(x228) d. Find P(22.1 sx 26.8). P(22.1 x 26.8) e. Find P(xs28.2) PK s28.2)(Round to four decimal places as needed.) O 1,2 | (Round to four decimal places as needed.) 15 ] (Round to four decimal places as needed.) f. Find P(x227.0). P 270)- Do1 (Round to four decimal plaoes as needed) P(x 27.0) = 1: Normal Curve Areas 1bo B 100.00 106-3R I

Explanation / Answer

(c) P(X > 28)

Since = 30 and = 2.2 we have:

P ( X > 28 ) = P ( X > 2830 ) = P ( X/ > 2830/2.2)

Since Z = x/ and 2830/2.2 = 0.91 we have:

P ( X > 28 ) = P ( Z > 0.91 )

Use the standard normal table to conclude that:

P (Z > 0.91) = 0.8186

(d) Same steps as above -

P ( 22.1 < X < 26.8 ) = P ( 3.59 < Z < 1.45 )

Use the standard normal table to conclude that:

P ( 3.59 < Z < 1.45 ) = 0.0733

(e)

P (X < 28.2) = P (Z < 0.82)

Use the standard normal table to conclude that:

P (Z < 0.82) = 0.2061

(f)

P ( X > 27.0 ) = P ( Z > 1.36 )

Use the standard normal table to conclude that:

P (Z > 1.36) = 0.9131

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