Question

# A normal population has a mean of 10.2 and a standard deviation of 1.4. Refer to...

A normal population has a mean of 10.2 and a standard deviation of 1.4. 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 10.2 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

Solution :

Given that ,

mean = = 10.2

standard deviation = = 1.4

(a)

x = 14.3

z = (x - ) / = (14.3 - 10.2) / 1.4 = 4.1 / 1.4 = 2.93

z = 2.93

(b)

P(10.2 < x < 14.3) = P((10.2 - 10.2)/ 1.4) < (x - ) / < (14.3 - 10.2) / 1.4) )

= P(0 < z < 2.93)

= P(z < 2.93) - P(z < 0)

= 0.9983 - 0.5

= 0.4983

Proportion = 0.4983

(c)

P(x < 10) = P((x - ) / < (10 - 10.2) / 1.4)

= P(z < -0.14)

= 0.4443

Proportion = 0.4443

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