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**Create a table for the equation:**

*y= 2*^{x}

**In Desmos, type in the coordinates:**

(1,3) (9,2)

(3,1)

(0,1) (, 1,0)

(-1, 0.333) (0.333, -1)

**What is their relationship between x and y coordinates?**

In desmos, type in the coordinates:

(0.04, -2)

(0.2, -1)

(1,0)

(5,1)

(25,2)

(125, 3)

What relationship do you see between the x and y coordinates?

An insurance company rounds 50000 insurance premiums to the nearest dollar. Assuming that the fractional parts of the premiums are continuous and uniformly distributed between 0 and 1, compute the probability that the total amount owing will be altered by more than $60.

You may use R to assist you in answering this question, but you would need to list out all working details.

Consider the following data:

86 144 81 72 97 110 87 106 118 92

103 132 108 107 80 91 84 98 120 70

110 96 82 99 110 117 83 85 92 83

86 125 87 104 57 46 92 86 92 110

110 66 148 80 109 95 107 99 94 108

89 118 83 102 70 88 163 89 131 98

104 130 88 75 91 97 76 94 151 89

108 97 87 107 117 100 74 108 106 103

104 80 134 92 115 91 123 97 84 106

96 65 100 87 86 110 102 96 94 161

(a) Form a frequency table and plot a frequency distribution of this data.

(b) Calculate the mean value of the data.

(c) Find the equation for the normal distribution that would fit the data as closely as possible.

(d) Plot the normal distribution curve that is described by this equation.

The diameters of the spores of lycopodium can be found by an interference method. The results of such an experiment are given below. The constant factor k = 5880 when the diameters are measured in cm

the following is the table

k x diameter (cm) :14 15 16 17 18 19 20 21 22 23

Number of spores :1 1 8 24 48 58 35 16 8 1

(a) Find the mean diameter of the spores.

(b) Calculate the standard deviation from the mean.

(c) Draw a normalised histogram of the data. (d) Plot the corresponding normal frequency curve on the same set of axes.

A group of 100 individuals each made an estimate of the interpolation of the readings of a scale instrument. The values of the estimates and the number of individuals who made the same estimate are tabulated below.

Reading : 6.2 6.3 6.4 6.5 6.6 6.7 6.8

Number of individuals : 4 11 18 24 21 14 8

(a) Draw the relative frequency curve.

(b) Calculate: i. the mean

ii. the standard deviation from the mean

suppose that 3000 drivers in wakanda were randomly breath tested on 21 april 2019 and 116 were above the limit of 0.05 blood alcohol level. on 15 may 2019,4000 drivers were tested and 98 were above this level

1.1 what additional information would you require before trying to conclusion