Question

1. According to a survey conducted in the Republic of KXW, the income distribution of all its union workers is normal with an average of 51000 KXW dollars and a standard derivation of 2700 KXW dollars. If a single worker is selected at random, use the normal distribution and compute the following: a. The probability that he/she earns more than 57000 KXW dollars b. The probability that he/she earns less than 47000 KXW dollars c. The probability that he/she earns between 47000 KXW dollars and 57000 KXW dollars

Answer 1

Area under normal curve will be used to find the required probability

a. The probability that he/she earns more than 57000 KXW dollars , Z > (57,000-51,000)/2,700

Z > 2.22

= 0.5 - 0.4864

= 0.0136 or 1.36%

b. The probability that he/she earns less than 47000 KXW dollars , Z < (47,000-51,000)/2,700

Z > -.148

=0.5 - 0.4306

= 0.0694 or 6.94%

c. The probability that he/she earns between 47000 KXW dollars and 57000 KXW dollars

= 0.4306 + 0.4864

= 0.917 or 91.7%