A random sample of n = 81 observations is drawn from a population with a mean eq

Question

A random sample of n = 81 observations is drawn from a population with a mean equal to 55 and a standard deviation equal to 36 a. Find the probability that x is less than 47 b. Find the probability that x is greater than 65. c. Find the probability that x falls between 47 and 67 Click the icon to view the table of normal curve areas. a. The probability that x is less than 47 is (Round to three decimal places as needed.) b. The probability that x is greater than 65 is Round to three decimal places as needed.) c. The probability that x falls between 47 and 67 is Round to three decimal places as needed.)

Explanation / Answer

Solution:- n = 81 , mean = 55 , sd = 36

Formula => Z = (X - )/(/sqrt(n))

a) The probability that X is less than 47 is  0.023

=> P(X < 47) = P(Z < (47-55)/(36/sqrt(81))

= P(Z < -2)

= 1 P(Z < 2)

= 1 - 0.9772

= 0.0228

= 0.023(rounded)

b) The probability that X is greather than 65 is  0.006

     => P(X > 65) = P(Z > (65-55)/(36/sqrt(81))

= P(Z > 2.5)

= 1 P(Z < 2.5)

= 1 0.9938

= 0.0062

= 0.006

c. The probability that X has between 47 and 67 is 0.976

   => P(47 < X < 67) = P( (47-55)/(36/sqrt(81)) < Z <  (67-55)/(36/sqrt(81)))

= P(-2 < Z < 3)

= 0.9759

= 0.976(rounded)

  

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