The random variable X is normally distributed. Also, it is known that P(X > 141)

ID: 3321436 • Letter: T

Question

The random variable X is normally distributed. Also, it is known that P(X > 141) = 0.09. Use Table 1.

a. Find the population mean if the population standard deviation = 12. (Round "z" value and final answer to 2 decimal places.)

b. Find the population mean if the population standard deviation = 27. (Round "z" value and final answer to 2 decimal places.)

c. Find the population standard deviation if the population mean = 120. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

d. Find the population standard deviation if the population mean = 113. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

solution=

given

P(X > 141) = 0.09

using z score table( 1 - 0.535856 = 0.464144

a) Find the population mean if the population standard deviation = 12

P(X > 141)= 0.4641

141 - / 12 = 0.4641

141 - = 12 * 0.4641

= 141 - 5.5692

= 135.43

b. Find the population mean if the population standard deviation = 27.

141 - / 27 = 0.4641

141 - = 27 * 0.4641

= 141 - 12.5307

= 128.47

c. Find the population standard deviation if the population mean = 120

141 - 120 / = 0.4641

=141 - 120 / 0.4641

=45.25

d. Find the population standard deviation if the population mean = 113?

141 - 113 / = 0.4641

=141 - 113 / 0.4641

= 60.33

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