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QUESTION 19 Sale SHS, wyremally distried with a 80 and standard deviation and the mean and standard deviation of students fin
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Answer #1

We have to deal with score at Statistical Methods I :

Here X ~ N(\small \mu = 80, \small \sigma =8)

Note that,

\small Let \ Z=\frac{X-\mu}{\sigma}\sim N(0,1)

\small P(Z\le z)=\Phi(z) \ and \ \Phi(-z)=1-\Phi(z)

Given that,

\small P(X>k)=0.9842

or, \ 1-P(\frac{X-\mu}{\sigma}\le \frac{k-80}{8})=0.9842

or, \ \Phi(\frac{k-80}{8})=0.0158=\Phi(-2.15)       (Value from z table)

or, \ \frac{k-80}{8}=-2.15

or, \ k=62.8

Therefore, the value of k is 62.8.

z table :

Z 0.0 0.1 02 03 0.4 05 0.6 0.7 0.8 0.9 1.0 1.1 12 13 14 15 1.6 17 18 1.9 2.0 21 22 23 2.4 25 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3

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