Scientists at the Hopkins Memorial Forest in western Massachusetts have been collecting meteorological and environ- mental data in the forest data for more than 100 years. In the past few years, sulfate content in water samples from Birch Brook has averaged 7.48 mg/L with a standard deviation of 1.60 mg/L. (a) What is the standard error of the sulfate in a collection of 10 water samples? (b) If 10 students measure the sulfate in their samples, what is the probability that their average sulfate will be between 6.49 and 8.47 mg/L? (c) What do you need to assume for the probability calculated in (b) to be accurate?

(a) standard error of the sulfate in a collection of 10 water samples = .506 mg/L

( b) the probability that their average sulfate will be between 6.49 and 8.47 mg/L = .950 mg/L

(c) We need to assume sample is random and normal sampling distribution probability calculated in (b) to be accurate.

Step-by-step explanation:

Given -

Average sulfate content = 7.48 mg/L

Standard deviation = 1.60 mg/L

(a) standard error of the sulfate in a collection of 10 water samples =

  standard error =  =   = .506 mg/L

(b) If 10 students measure the sulfate in their samples, what is the probability that their average sulfate will be between 6.49 and 8.47 mg/L =

=

                               =

                               =

                               = .975 - .025 = .950 mg/L

(c) We need to assume sample is random and normal sampling distribution probability calculated in (b) to be accurate.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x