Question

Game times in a recent basketball season were normally​ distributed, with a mean of 115.5 minutes and a standard deviation of 12.7 minutes. Find the probability that a randomly selected game lasted between 79.3 and 150.6 minutes. Show or explain how to find the​ answer, and give the final probability rounded to four decimal places.

Answer 1

Solution :

Given that ,

mean = = 115.5

standard deviation = = 12.7

P(79.3 < x < 150.6) = P((79.3 - 115.5)/ 12.7) < (x - ) /  < (150.6 - 115.5) / 12.7) )

= P(-2.85 < z < 2.76)

= P(z < 2.76) - P(z < -2.85)

= 0.9971 - 0.0022 Using standard normal table,  

Probability = 0.9949