Question

A normal population has a mean of 11.8 and a standard deviation of 4.6. Refer to the table in Appendix B.1.  

a. Compute the z-value associated with 14.3. (Round the final answer to 2 decimal places.)

z =           

  

b. What proportion of the population is between 11.8 and 14.3? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.)

Proportion           

c. What proportion of the population is less than 10.0? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.)

Proportion           

Answer 1

solution:-

given that mean = 11.8 , standard deviation = 4.6

formula z = (x-mean)/standard deviation

a. the z-value associated with 14.3

=> z = (14.3-11.8)/4.6

=> z = 0.54

b. What proportion of the population is between 11.8 and 14.3

=> P(11.8 < x < 14.3)

=> P((11.8-11.8)/4.6 < z < (14.3-11.8)/4.6)

=> P(0 < z < 0.54)

=> P(z < 0.54) - P(z < 0)

=> 0.7054 - 0.5

=> 0.2054

c. What proportion of the population is less than 10.0

=> P(x < 10.0)

=> P(z < (10.0-11.8)/4.6)

=> P(z < -0.39)

=> 1 - P(z < 0.39)

=> 1 - 0.6517

=> 0.3483