Create a vector named iq of 100 elements of n(100,20) (normal with a mean of 100 and std dev of 20) data. 6. add 10 to every element of iq 7. calculate the mean and std dev of iq?

See code and explanation below.

Step-by-step explanation:

For this case we can use the following R code to create a vector of 100 elements from a normal distribution given by:

The function rnorm creates a sample data from the normla distribution with the mean and deviation provided

> normal<-rnorm(100,mean = 100,sd=20)

We can visualize the data like this

> normal

 [1]  87.47092 103.67287  83.28743 131.90562 106.59016  83.59063 109.74858 114.76649 111.51563

[10]  93.89223 130.23562 107.79686  87.57519  55.70600 122.49862  99.10133  99.67619 118.87672

[19] 116.42442 111.87803 118.37955 115.64273 101.49130  60.21297 112.39651  98.87743  96.88409

[28]  70.58495  90.43700 108.35883 127.17359  97.94425 107.75343  98.92390  72.45881  91.70011

[37]  92.11420  98.81373 122.00051 115.26351  96.70953  94.93277 113.93927 111.13326  86.22489

[46]  85.85010 107.29164 115.37066  97.75308 117.62215 107.96212  87.75947 106.82239  77.41274

[55] 128.66047 139.60800  92.65557  79.11731 111.39439  97.29891 148.03236  99.21520 113.79479

[64] 100.56004  85.13454 103.77585  63.90083 129.31110 103.06507 143.45223 109.51019  85.80107

[73] 112.21453  81.31805  74.92733 105.82892  91.13416 100.02211 101.48683  88.20958  88.62663

[82]  97.29643 123.56174  69.52866 111.87892 106.65901 121.26200  93.91632 107.40038 105.34198

[91]  89.14960 124.15736 123.20805 114.00427 131.73667 111.16973  74.46816  88.53469  75.50775

[100]  90.53199

Then we can add 10 to each element of the vector like this:

> normal1<-normal+10

And we can visualize the results like this

> normal1

 [1]  97.47092 113.67287  93.28743 141.90562 116.59016  93.59063 119.74858 124.76649 121.51563

[10] 103.89223 140.23562 117.79686  97.57519  65.70600 132.49862 109.10133 109.67619 128.87672

[19] 126.42442 121.87803 128.37955 125.64273 111.49130  70.21297 122.39651 108.87743 106.88409

[28]  80.58495 100.43700 118.35883 137.17359 107.94425 117.75343 108.92390  82.45881 101.70011

[37] 102.11420 108.81373 132.00051 125.26351 106.70953 104.93277 123.93927 121.13326  96.22489

[46]  95.85010 117.29164 125.37066 107.75308 127.62215 117.96212  97.75947 116.82239  87.41274

[55] 138.66047 149.60800 102.65557  89.11731 121.39439 107.29891 158.03236 109.21520 123.79479

[64] 110.56004  95.13454 113.77585  73.90083 139.31110 113.06507 153.45223 119.51019  95.80107

[73] 122.21453  91.31805  84.92733 115.82892 101.13416 110.02211 111.48683  98.20958  98.62663

[82] 107.29643 133.56174  79.52866 121.87892 116.65901 131.26200 103.91632 117.40038 115.34198

[91]  99.14960 134.15736 133.20805 124.00427 141.73667 121.16973  84.46816  98.53469  85.50775

[100] 100.53199

The sample mean is given by:

And the sample deviation by:

If we want to calculate the mean and standard deviation for the original data we can do this:

> mean(normal)

[1] 102.1777

And the standard deviation with:

> sd(normal)

[1] 17.96399

Other way to calculate the deviation is:

> sqrt(sum((normal-mean(normal))^2/(length(normal)-1)))

[1] 17.96399

answer:

c. the third graph

b

step-by-step explanation: