Question

Sports that involve a significant amount of running, jumping, or hopping put athletes at risk for Achilles Tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in a medical journal looked at the diameter (in mm) of the affected and nonaffected 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 5.94 millimetres (mm) with a standard deviation of 1.92 mm. What average tendon diameters should we see 80% of the time in any random sample of 31 drawn from the general population?

Answer 1

solution:

Given that,

mean = = 5.94

standard deviation = = 1.92

n = 31

= 5.94

= / n = 1.92 /31=0.34

Using standard normal table,

P(Z < z) = 80%

= P(Z < z) = 0.80  

= P(Z <0.84 ) = 0.80

z =0.84    Using standard normal table,

Using z-score formula  

= z * +   

= 0.84 *0.34+5.94

= 6.2256

= 6.23 rounded