Question

Sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study looked at the diameter (in mm) of the injured and healthy tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of 5.99 millimeters (mm) with a standard deviation of 1.96 mm.

(a)

What is the probability that a randomly selected sample of 30 patients would produce an average diameter of 6.8 mm or less for the nonaffected tendon? (Round your answer to four decimal places.)

(b)

When the diameters of the affected tendon were measured for a sample of 30 patients, the average diameter was 9.8. If the average tendon diameter in the population of patients with AT is no different than the average diameter of the nonaffected tendons (5.99 mm), what is the probability of observing an average diameter of 9.8 or higher? (Round your answer to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 5.99

standard deviation = = 1.96

n = 30

=    = 5.99

= / n = 1.96/ 30 = 0.3578

a) P( 6.8) = P(( - ) / (6.8 - 5.99) / 0.3578)

= P(z 2.26)

Using z table

= 0.9881

b) P( 9.8 ) = 1 - P( 9.8 )

= 1 - P[( - ) / (9.8 - 5.99) / 0.3578 ]

= 1 - P(z 10.65)

Using z table,    

= 1 - 1

= 0