Tickets to minor league baseball games cost on average $7.02. Including food, dr

Question

Tickets to minor league baseball games cost on average $7.02. Including food, drinks, parking, and other expenses, the average cost for a family of four to attend the game is $57.70. Assume the distribution of cost has a normal distribution with standard deviation $5.57. The approximate proportion (using the standard normal table) of people that will pay between $60 and $70 is: A. 0.0136. B. 0.6591. C. 0.9864. D. 0.3273 Tickets to minor league baseball games cost on average $7.02. Including food, drinks, parking, and other expenses, the average cost for a family of four to attend the game is $57.70. Assume the distribution of cost has a normal distribution with standard deviation $5.57. The approximate proportion (using the standard normal table) of people that will pay between $60 and $70 is: A. 0.0136. B. 0.6591. C. 0.9864. D. 0.3273

Explanation / Answer

Normal Distribution
Mean ( u ) =57.7
Standard Deviation ( sd )=5.57
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 60) = (60-57.7)/5.57
= 2.3/5.57 = 0.4129
= P ( Z <0.4129) From Standard Normal Table
= 0.66017
P(X < 70) = (70-57.7)/5.57
= 12.3/5.57 = 2.2083
= P ( Z <2.2083) From Standard Normal Table
= 0.98639
P(60 < X < 70) = 0.98639-0.66017 = 0.3263 ~ nearest value is 0.3273 as per options
          

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