Question

1. Please find the with the following data set:

21

28

38

45

47

51

58

67

71

71

standard deviation=  

A new number, 199, is added to the data set above. Please find the new range, sample standard deviation, and IQR of the new data set.

standard deviation =  

2. The length of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51 and 51.2 min.

P(51 < X < 51.2) =

You must draw a sketch of the distribution, with the area representing the probability you are finding shaded, and all-important values marked on both axes. You also need to show your calculation. Include this sketch and calculation with the work that you upload for the test and be sure to include the question number.

60% of all Americans are homeowners. If 36 Americans are randomly selected, find the probability that

a. Exactly 20 of them are homeowners.
b. At most 22 of them are homeowners.
c. At least 20 of them are homeowners.

Answer 1

1) = (21 + 28 + 38 + 45 + 47 + 51 + 58 + 67 + 71 + 71)/10 = 49.7

s = sqrt(((21 - 49.7)^2 + (28 - 49.7)^2 + (38 - 49.7)^2 + (45 - 49.7)^2 + (47 - 49.7)^2 + (51 - 49.7)^2 + (58 - 49.7)^2 + (67 - 49.7)^2 + (71 - 49.7)^2 + (71 - 49.7)^2)/9) = 17.44

After adding 199 to the data set, we will get

21, 28, 38, 45, 47, 51, 58, 67, 71, 71, 199

Range = 199 - 21 = 178

= (21 + 28 + 38 + 45 + 47 + 51 + 58 + 67 + 71 + 71 + 199)/11 = 63.27

s = sqrt(((21 - 63.27)^2 + (28 - 63.27)^2 + (38 - 63.27)^2 + (45 - 63.27)^2 + (47 - 63.27)^2 + (51 - 63.27)^2 + (58 - 63.27)^2 + (67 - 63.27)^2 + (71 - 63.27)^2+ (71 - 63.27)^2 + (199 - 63.27)^2)/10) = 47.96

Q1 = 38

Q2 = 51

Q3 = 71

IQR = Q3 - Q1 = 71 - 38 = 33

2) P(51 < X < 51.2)

= (51.2 - 51)/(52 - 50)

= 0.2/2 = 0.1

3) n = 36

    p = 0.6

= np = 36 * 0.6 = 21.6

= sqrt(np(1 - p))

    = sqrt(36 * 0.6 * 0.4)

    = 2.94

a) P(X = 20)

= P((19.5 - )/< (X - )/< (20.5 - )/)

= P((19.5 - 21.6)/2.94 < Z < (20.5 - 21.6)/2.94)

= P(-0.71 < Z < -037)

= P(Z < -0.37) - P(Z < -0.71)

= 0.3557 - 0.2389

= 0.1168

b) P(X < 22)

= P((X - )/< (22.5 - )/)

= P(Z < (22.5 - 21.6)/2.94)

= P(Z < 0.31)

= 0.6217

c) P(X > 20)

= P((X - )/> (19.5 - )/)

= P(Z > (19.5 - 21.6)/2.94)

= P(Z > -0.71)

= 1 - P(Z < -0.71)

= 1 - 0.2389

= 0.7611