Question

A study shows that the lengths of the careers of professional football players are nearly normally distributed, with a mean of 6.2 years and a standard deviation of 1.9 years.

(a) What percent of professional football players have a career of more than 9 years? (Round your answer to one decimal place.) %

(b) If a professional football player is chosen at random, what is the probability that the player will have a career of between 3 and 4 years? (Round your answer to three decimal places.)

Answer 1

Solution :

Given that ,

mean = = 6.2

standard deviation = = 1.9

P(x >9 ) = 1 - P(x< 9)

= 1 - P[(x -) / < (9 -6.2) /1.9 ]

= 1 - P(z <1.47 )

Using z table

= 1 - 0.9292

= 0.0708

answer=7.1%

(B)

P(3< x <4 ) = P[(3 -6.2) /1.9 < (x - ) / < (4 -6.2) / 1.9)]

= P(-1.68 < Z < -1.16)

= P(Z < -1.16) - P(Z < -1.68)

Using z table   

= 0.1230-0.0465

   probability= 0.077