The cost of 5 gallons of ice cream has a variance of 49 with a mean of 37 dollars during the summer. What is the probability that the sample mean would be less than 35.2 dollars if a sample of 77 5-gallon pails is randomly selected

P ( Z < 35,2 )  =  0,0122    or   1,22 %

Step-by-step explanation:

Assuming a normal distribution:

μ = 37

σ²  =  49       σ  =  7

Z(s) =  (  x  -  μ  ) / σ /√n

Z(s) = ( 35.2  -  37 ) / 7 / √77

Z(s) =  - 1.8 * 8.77 / 7

Z(s)  =  -  2.25

From z- table we find the area under the bell shape curve and it is:

0,0122

Then  P ( Z < 35,2 )  =  0,0122    or   1,22 %

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