PRACTICE ANOTHER The administration of a large university wants to take a random sample to measure student opinion of a new food service on campus. It plans to use a scale from 1 to 100, on which 1 is complete dissatisfaction and 100 is complete satisfaction. The administration knows from past experience with such questions that the standard deviation for the responses is going to be about 3, but it does not know what to expect for the mean. It wants to be almost sure that the sample mean is within plus or minus 1 point of the true population mean value. How large, n will the random sample have to be

81 samples

Step-by-step explanation:

According to the empirical rule :

Possible values of the sample mean is within 3 standard deviations of the population mean :

μ ± 3 sd(x) ; sd(x) = standard deviation of sampling distribution.

3 * sd(x) = 1

sd(x) = 1/3

Recall:

Standard deviation of sampling distribution, sd(x)

sd(x) = σ / sqrt(n)

1/3 = 3 / sqrt(n)

Square both sides

1/9 = 9/n

Cross multiply :

n * 1 = 9 * 9

n = 81

"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: