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Regarding the data-set of the temperatures, it is found that:a) The mean and the standard deviation are given as follows:Mean: 80.41Standard deviation: 8.33.b) The histogram is bell shaped.c) 95% of the days will be between 63.75 ºF and 97.07 ºF.How to obtain the mean and the standard deviation?The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.The number of observations is:5 + 309 + 1496 + 1521 + 533 + 6 = 3870.Considering the midpoint of each interval, the following distribution is built:P(X = 54.5) = 5/3870 = 0.0013.P(X = 64.5) = 309/3870 = 0.0798.P(X = 74.5) = 1496/3870 = 0.3866.P(X = 84.5) = 1521/3870 = 0.3930.P(X = 94.5) = 533/3870 = 0.1377.P(X = 104.5) = 6/3870 = 0.0016.The mean is given by the sum of each value multiplied by it's relative frequency, hence:E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:80.41 - 2 x 8.33 = 63.75.80.41 + 2 x 8.33 = 97.07.More can be learned about the Empirical Rule at https://brainly.com/question/10093236#SPJ1
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