The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is 0.8132.
Let x be the total amount spent by students.
x follows normal distribution with mean μ = 650,
                                   standard deviation δ = 120
We take a simple random sample of size n = 10
We are asked to find average spending of 10 students (  ) is between 600 and 700
 ) is between 600 and 700
We have to find P( 600 <=  <= 700)
 <= 700)
According to the sampling distribution of the sample mean  , it follows an approximately normal distribution with mean μ{
, it follows an approximately normal distribution with mean μ{ } = μ and standard deviation  δ{
} = μ and standard deviation  δ{ } = {δ}/{√n}
} = {δ}/{√n}
Therefore here mean of  ,( μ{
,( μ{ } ) = 650 and
} ) = 650 and
standard deviation of  , δ{
, δ{ } = {120}/{√10} = 37.9473
} = {120}/{√10} = 37.9473
The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is,
Let Z= x - μ / δ 
Z₁ = 600 - 650 / 37.9473 = -1.32 similarly 
Z₂ = 700 - 650 / 37.9473 = 1.32
From standard normal distribution table, P( -1.32 <   <  1.32) = 0.8132
  <  1.32) = 0.8132
The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is 0.8132
To learn more about Normal distribution click here:
brainly.com/question/15103234
#SPJ4