1) What is symmetric distribution of data, left-skewed distribution of data and right-skewed distribution of data?
2) Create frequency distribution of the following data set.
13 17 13 22 17 22 17 13 14 16 18 20 10 18 10 16 20 14 16 16
Explain the shape of the distribution.
3) The scores in Mathematics of 15 students are given below. Find range, sample variance and standard deviation.
93 85 78 79 97 90 82 61 53 63 94 69 84 67 95
Show and explain your steps.
4) Find the population variance and standard deviation for the grouped frequency distribution of the following data set.
Class Frequency
60-62 5
63-65 18
66-68 42
69-71 27
72-74 8
5. Describe empirical rule relative to normal distribution. What is standard normal distribution?
6. A random sample of 100 apples was taken from an orchard and individual weights were measured. The mean and variance of these measurements were 6.8 ounces and .64 (ounces)2, respectively. Fill in the blanks using empirical rule, assuming the measurements produced a normal distribution.
a. 68 % of measurements lie in the interval from ________ to _______.
b. 95 % of measurements lie in the interval from ________ to _______.
c. 99.7% of measurements lie in the interval from ________ to _______.
7) Using the scores of #3 how many scores were within one standard deviation of mean, two standard deviation of mean and three standard deviation of mean.
8) What is z-score and how do you find the area under standard normal distribution curve.
a) Find the area under the normal distribution curve between z=0 and z=2.34.
b) Find the area under the normal distribution curve between z=0 and z=-1.75.
c) Find the probability P(-1.75
9) A student received a grade of 95 in Mathematics test for which mean grade is 85 and standard deviation is 12.On a Physics test he received a grade of 92 for which mean grade is 84 and standard deviation was 15.In which subject his relative standing is higher and why?
10) The following are the prices charged (in cents) for a can of chicken soup at 20 super markets.
80 89 81 78 92 82 79 85 79 85 91 80 81 84 90 79 79 78 92 84
a) Calculate the mean and standard deviation.
b) What percentage of data lies in the interval μ ± σ ? In the interval μ ± 2σ ?
Do the results agree with the empirical rule (approximately).