When Sam goes to a restaurant, he always tips the sener $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution

Question

When Sam goes to a restaurant, he always tips the sener $2 plus 10% of the cost of the meal. If Sam&#039;s distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution

skilningugdK · Accepted Answer

Let X be the random variable which represents the meal costsThen ,  E  (  X  )  =  9     and  s  d  (  X  )  =  3     i  .  e  ;  Var  (  X  )  =  9The random variable representing the Tips is  2 + 10% of X i.e; 2+0.1X.Then,  E  (  0.1  X  +  2  )  =  0.1  E  (  X  )  +  2  =  0.1  (  9  )  +  2  =  2.9and  Var  (  0.1  X  +  2  )  =  (  0.1      )    2    Var  (  X  )  =  (  0.01  )  (  9  )  =  0.09    ⇒  s  d  (  0.1  X  +  2  )  =      Var(0.1X+2)    =      0.09    =  0.3