question is in description (statistics)

Question

The times per workout an athlete uses a stairclimber are normally distributed, with a mean of 20 minutes and a standard deviation of 5 minutes. An athlete is randomly selected. Find the probability that the athlete uses a stairclimber between 20 and 28 minutes. 

Answer 1

Hi Cameron.

 

To answer this you will need a Standard Normal Distribution table.  

 

The probability can be represented as  P(20<X<28).  To find it though, we need to shift this down to where we can look it up on the table with z-scores.  

 

Z is defined as   Z=(X-μ)/σ   

 

Your Z_low corresponds to the data point 20 minutes, found in P(20<X<28).  Z_lo=(20-20)/5 = 0

Your Z_high corresponds to the data point 28 minutes found in P(20<X<28).  Z_HI = (28-20)/5 = 1.6

 

So instead of P(20<X<28) we will use P(0 < Z < 1.6)

 

On the table look up Z = 1.6    you should find that it is 0.9452

On the table look up Z = 0       you should find that it is 0.5000

 

Now subtract:   0.9452 - 0.5000 = 0.4452   <--- this is the probability that the athlete uses a stairclimber between 20 and 28 minutes (for a mean of 20 and a standard deviation of 5).

 

FINAL ANSWER:  0.4452 is the probability.

 

(If they had asked for a percent, it would be 44.52%, if they had asked for a fraction it would have been (4452/10000) which reduces to 1113/2500