Question

The mean annual salary for a secondary school teacher in the UK is 29,496 pounds. What is the probability that a teacher’s annual salary is between 28,987 pounds and 31,562 pounds? Assume the salaries are normally distributed and that the standard deviation for all salaries is 1,131 pounds.

Use the tables in the book and not an outside source.

Please show work for the opportunity to earn partial credit on this question.

Answer 1

Solution :

Given that,

mean = = 29496

standard deviation = = 15

P ( 28987 < x < 31562 )

P ( 28987- 29496 / 1131 ) < ( x -  / ) < ( 31562 - 29496 / 1131)

P ( -509 / 1131 < z < 2066 / 1131)

P (-0.45 < z < 1.83 )

P ( z < 1.83 ) - P ( z < -0.45 )

Using z table

= 0.9664 - 0.3264

= 0.6400

Probability = 0.6400