Question

Consider a box containing the following numbers.

3, 5, 10, 14, 17

The SD for the box is 5.27.

Suppose 100 draws are made at random with replacement from the box.

The expected value for the average of the draws is ___ give or take ___

Find the chance that the average of the draws is less than 10.33. ___

Find the chance that the average of the draws is between 9.27 and 10.33. ___

Answer 1

here expected value =(3+5+10+14+17)/5=9.8

standard deviation σ=	5.27000
sample size       =n=	100
std error=σx̅=σ/√n=	0.527

The expected value for the average of the draws is 9.8  give or take 0.527

2)from normal approximation:

probability =P(X<10.33)=(Z<(10.33-9.8)/0.527)=P(Z<1.01)=0.8438

(please try 0.8427 if required from ti-84)

3)

probability =P(9.27<X<10.33)=P((9.27-9.8)/0.527)<Z<(10.33-9.8)/0.527)=P(-1.01<Z<1.01)=0.8438-0.1562=0.6876

(please try 0.6854 if required from ti-84)