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

Ada Lloyd

Ada Lloyd

Answered question

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

Beginner2022-11-28Added 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?