Using appropriate secondary data from a reliable source, students are expected to demonstrate their understanding on continuous probability distribution by the following details:

1. Determination of normality of the data and the shape of the distribution.

2. Demonstration of transformation to standard normal distribution.

3. Finding the probability of certain range of values.

4. Demonstration of understanding of confidence intervals. Relate the explanation to the dataset selected.

Detailed explanation, working and diagram are expected whenever necessary.

may I have an idea on how to do the question? with numbered example? really need help on this, thank you

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you take any data on your book and apply the concept that we demonstrate below -(1) for normally checking you use two method.(i) Histagram(2) Q-Q-plat(3) Box-platIn thistogream you plot diagram between class-interval and frequency. So you make your class interval and related frequency from dataIn Q-Q-plat you draw reliclual of data and see there is a straight line or meetIf error fluetuates more from straight line then it data does not comes from normal pop"In Bor-plat, you find some basic measure of control tendency and measure of disperson like as median, first quartile, third quartile, Min & Maximum and draw Box-plate.If boxplat like as below(2) for changing standard Normal distribution. we calculate Expectation and standard devision of random variable ($ay \left.x_{i}\right) & transformlike as\frac{x_{i}^{0}-E\left(x_{i}^{0}\right)}{\sqrt{V\left(x_{i}\right)}} \sim N(0,1)(3) far finding probability at certain range we have to change in standard Normal dist ^{n} & then find probability b/w 0 to like as\begin{array}{l}P\left(x_{1}<x_{i}<x_{2}\right) \\P\left(\frac{x_{1}-f\left(x_{i}\right)}{\sqrt{v\left(x_{i}\right)}}<z<\frac{x_{2}-E\left(x_{i}\right)}{\sqrt{v\left(x_{i}\right)}}\right. \\P\left(P_{1}<z<P_{2}\right)\end{array}as Narmal dist is symmetric so\Rightarrow 2 \times P\left[0<z<p_{2}\right] Nowsee this value from Normal table.(4) Confidence interval is an interval which contain \left(100(1-\alpha) \%\right. of pop { }^{n} parameter.for finding confidence interval,we find photal quantity and let T_{1} and T_{2} be two statisfic thenP\left(T_{1} \leqslant \text { pivotal quantity }<T_{2}\right]=1-\alphathen \left(T_{1} T_{2}\right) are the C.I at \left.10011-\alpha\right) \% confidence level. ...