Answer to Question #344886 in Statistics and Probability for Akshay

Question

EA Sports have asked you (an analyst) to find out the mean and standard deviation of the number of minutes people take to complete level 1 of their new game using the below information: The number of minutes people spend playing level 1 follows a normal distribution The probability of player playing for less than 5 minutes is 0.0045 The probability of someone taking less than 15 minutes to complete level 1 is 0.9641

Answer 1

$$P(X<5)=P(Z<\dfrac{5-\mu}{\sigma})=0.0045$$

$$\dfrac{5-\mu}{\sigma}=-2.612054$$

$$P(X<15)=P(Z<\dfrac{15-\mu}{\sigma})=0.9641$$

$$\dfrac{15-\mu}{\sigma}=1.800384$$

$$\dfrac{5-\mu}{15-\mu}=\dfrac{-2.612054}{1.800384}$$

$$\mu=\dfrac{5(1.800384)+15(2.612054)}{1.800384+2.612054}$$

$$\mu=10.92$$

$$\sigma=\dfrac{15-10.92}{1.800384}$$

$$\sigma=2.266$$