A researcher measures his patients' sleep times in minutes for a study in his thesis. For a group of 10 patients, the records are as follows: 90 180 280 450 550 580 600 690 720 940 Calculate the following: a) The mean b) The median c) The mode d) The maximum and the minimum e) The range f) Quartiles B) The IQR h) The Five number summary i) Outliers j) Draw a box plot for this batch and label important measures. The mean height of 15 to 20-year-old males from Turkey from 2019 to 2020 was 178 cm with a standard deviation of 5 cm. Male heights are known to follow a normal distribution. a. Find the probability that a randomly chosen 15-to 20-year-old male from Turkey has height of more than 190, using the STD table. b. Find the probability that a randomly chosen 15- to 20-year-old male from Turkey has a height of less than 160, using the STD table. c. Find the probability that a randomly chosen 15-to 20-year-old male from Turkey has a height between 173 and 188, using the STD table. d. Explain part c, using Empirical Rule. e. Any 15 to 20-year-old male is considered to be extremely tall if he is in the top 3%. Find what makes a male extremely tall. Suppose that the distance of fly balls hit to the outfield (in baseball) is distributed with a mean of 375 feet and a standard deviation of 60 feet. We randomly sample 64 fly balls. a. Find the distribution of the sample with a size of 64. b. Find the probability that the mean of the sampling distribution of size is greater than 383. c. Find the probability that the distance of the sample size 64 has an average between 384.5 feet and 365.5 feet.