A basketball coach is looking over the possessions per game during last season. Assume that the possessions per game follows an unknown distribution with a mean of 56 points and a standard deviation of 12 points. The basketball coach believes it is unusual to score less than 50 points per game. To test this, she randomly selects 36 games. Use a calculator to find the probability that the sample mean is less than 50 points. Round your answer to three decimal places if necessary.

The probability that the sample mean is less than 50 points = 0.002    

Step-by-step explanation:

Step(i):-

Given mean of the normal distribution = 56 points

Given standard deviation of the normal distribution = 12 points

Random sample size 'n' = 36 games

Step(ii):-

Let x⁻ be the random variable of normal distribution

Let x⁻ = 50

The probability that the sample mean is less than 50 points

P( x⁻≤ 50) = P( Z≤-3)

                = 0.5 - P(-3 <z<0)

               = 0.5 -P(0<z<3)

               =  0.5 - 0.498

               = 0.002

Final answer:-

The probability that the sample mean is less than 50 points = 0.002

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