Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. A. 91.68 B. 92.03 < μ < 97.97
C. 92.95 D. 91.69 < μ < 98.31

B) 92.03 < μ < 97.97

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Step-by-step explanation:

Step(i):-

Given sample mean (x⁻) = 95

standard deviation of the sample (s) = 6.6

Random sample size 'n' = 30

99% confidence interval for the mean score of all students.

step(ii):-

Degrees of freedom

ν =   n-1 = 30-1 =29

99% confidence interval for the mean score of all students.

( 95 - 2.966 , 95 + 2.966)

(92.03 , 97.97)

Final -

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

both equations and proportions are better.

"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: