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

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

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

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

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

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

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

$$\mu=10.92$$

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

$$\sigma=2.266$$