Asample of 81 calculus students at a large college had a mean mathematics act score of 26 with a standard deviation of 6. find a 95% confidence interval for the mean mathematics act score for all calculus students at this college.

24.67 ≤ μ ≤ 27.33

Step-by-step explanation:

From the information given: n = 81 students, Sample mean (x bar) = 26 and sample standard deviation (s) = 6.

Since the population standard deviation in unknown we use the student t distribution to estimate the mean. The mean is estimated as follows:

X bar - t (∝/2, n-1) x s/sqrt n ≤ μ ≤ X bar + t (∝/2, n-1) x s/sqrt n

Degrees of freedom, df = n - 1 = 81 - 1 = 80

∝ = 100 - 95 = 5% = 0.05   thus ∝/2 = 0.025

From the t distribution t (0.025,80) = 1.990

Substituting into the formula:

26 - 1.990 x 6/sqrt 81 ≤ μ ≤ 26 + 1.990 x 6/sqrt 81

24.67 ≤ μ ≤ 27.33

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: