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.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.