the result is the total of the following probabilities:

1/8 + 3/8 + 3/8 = 7/8

155 + 156 + 157 + 160 + 162 + 165 + 170 + 180 / 9= 161

The number of people in a mall can be countable while the other variables are measured.

a = 5 / (4 x 3) = 5 / 12 ; arithmetic mean : m = 70 / 5 = 14 ; s = ((4² + 2² + 2² + 2² + 6²) / 4)^1/2 = 4 ; standard coefficient of skewness SCS = (5 / 12) x ((4³ + 2³ + 2³ + 2³ + 6³) / 4³) = (5 / 12) ((64 + 24 + 216) / 64) = (5 / 12) (304 / 64) = (5 / 12) (76 / 16) = (5 / 12) (19 / 4) = 95 / 48. pg. 122. Correct answer is E.

According to empirical probability approach, what is the probability of obtaining a number 6 when you throw a six-sided fair die? Using the formula given before the probability we are looking for is:

P(Number 6) = 172/ 1000= 0.172

The correct answer is A.

The range of a data set, shown as R, is the difference between the largest and smallest values and calculated as follows: R = Largest Value - Smallest Value

R = 10-1 = 9.  The correct answer is B. 

Not cumulative distribution function but probability density function fulfils the property of f(x)≥0 for all x.

darkness is data, not variable. pg. 14. Correct answer is B.

The answer is E)46 as : The total scores are 230 and when we divide 230 by 5 we get 46 

The interquartile range IQR = P(75) – P(25) ; k1 = 20 x (75 / 100) = 15 ; P(75) = (1.800 + 2.000) / 2 = 1.900 ; k2 = 20 x (25 / 100) = 5 ; P(25) = (1.200 + 1.400) / 2 = 1.300 ; IQR = 1.900 – 1.300 = 600 . pg. 120. Correct answer is B.

The mean of an f(x) function is equal to the integral of that function's product to it's respective x on the given range. For the function f(x)= x for 0 ? x ? 3 the integral of x*f(x) on the range 0 to 4 is taken. This would yield to the integral of x² which is equal to x³/3. For x=0 this would equal to 0, for x=4 this would equal to 9. The mean is equal to 9 - 0 = 9. The answer is B.

Scatter plot is used to investigate the relationship between two variables. They are also very helpful indicating the minimum, maximum or outliers of the variables.The correct answer is D. 

­The range for grouped frequency distribution is calculated to be the difference of the upper limit of the highest value and the lower limit of the first class.

R=30-8=22

For a continuous random variable X, probability density function f (x) must satisfy the following
properties, 

(i) f (x) ? 0 for all x,

(ii) the integral of f(x) between positive infinite and negative infinite is equal to 1

(iii) P(a ? X ? b) is equal to the area under probability density function between points a and b.

The answer is A.

The median is 2 cigarettes. This means that 50% of the workers consume less than 2 cigarettes, and 50% of the workers consume more than 2 cigarettes. The 25th and 75th percentiles are 1 and 4 cigarettes, respectively. This means that 25% of the workers consume is either less than or equal to 1 cigarettes and 75% of the workers consume leither 4 or fewer than 4 cigarettes a day. The interquartile range is 4-1=3 cigarettes. This means that 50% of the workers consume 3 cigarettes. The highest and the lowest values within the upper and the lower boundaries for outliers are 8 and 0, respectively. There are outliers in the data. The values greater than 8 are the outliers. The shape of the distribution is right skewed, because the median line is closer to the 25th percentile and also the whisker over the 75th percentile is longer than the other whisker.The correct answer is C.

The median can also be estimated by using ogive curve (cumulative frequency polygon). The correct answer is C.

We can define probability distribution as a rule that assigns probabilities to the values of random variables.So the correct answer is D.