When Sam goes to a restaurant, he always tips the sener $2 plus 10% of...

Ada Lloyd

Ada Lloyd

Answered

2022-11-27

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

Answer & Explanation

skilningugdK

skilningugdK

Expert

2022-11-28Added 15 answers

Let X be the random variable which represents the meal costs
Then ,
E ( X ) = 9   and s d ( X ) = 3   i . e ; Var ( X ) = 9
The 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 = 2.9
and
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

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