Question

A) Research showed mean income of $48,000. Standard deviation was $10,000. What is the probability that someone earns less than $54,000?

B) Using information from the above question, what is the probability that a person would have more than $65,200?

Answer 1

Given,

= 48000

= 10000

1) p( x < 54000)

P(x < 54000) = 0.5 + p(0 < z < x-/​​​​​​)

= 0.5 + p(0< z < 54000-48000/10000)

= 0.5 + p( 0< z < 0.60)

= 0.5 + 0.2257

P(x < 54000) = 0.7257

Therefore probability that someone earn less than $54000 is 0.7257.

2) p(x> 65200) = 0.5 - p(0<z<65200-48000/10000)

= 0.5 - p(0< z < 1.72)

= 0.5 - 0.4573

P( x> 65200) = 0.0427

Therefore probability that person would have more than $65200 is 0.0427.