Question

introduction To Statistics (W118-19 Mat 102 JA) joshua melville &1 1/8/19 10:17 P uiz: Quiz 6 - Chapter 8 01.41.32 Submit O his Question: 1 pt 3 of 5 This Quiz: 5 pts poss utor to help them improve their results on a certain mathematical test. These students had p mean change in score of 19 points with a standard deviation of 65 points in a random sample of 100 who pay a private tutor to help them improve their results, what is the likelihood that the change in the sample mean score is less than 10 points? Click the loon to view the table of normal curve areas Px10)-(Round to three decimal places as needed)

Answer 1

Solution :

$\mu =19,$

$\sigma =65$

$\mathrm{and}$

$n =100$

$\mathrm{P}(\bar{x}<10)=\mathrm{P}(z<\frac{10-19}{\frac{65}{\sqrt{100}}})$

$=\mathrm{P}(z<\frac{-9}{\frac{65}{\sqrt{100}}})$

$=\mathrm{P}(z<-\frac{9\sqrt{100}}{65})$

$=\mathrm{P}(z<-\frac{9*\sqrt{2^2*5^2}}{65})$

$=\mathrm{P}(z<-\frac{9*\sqrt{2^2}\sqrt{5^2}}{65})$

$=\mathrm{P}(z<-\frac{9*2*5}{5*13})$

$=\mathrm{P}(z<-\frac{9*2}{13})$

$=\mathrm{P}(z<-\frac{18}{13})$

$=\mathrm{P}(z<-1.38})$

$=0.08379\approx 0.084$

$=0.084$