Question

Question 18 1 pts Use the following information for Questions 16 - 18. Question 18: For a population with a normal distribution and u = 70GPa and o = 1.6G Pa and n = 16, what is the probability that the sample mean is between 69 and 71? 0 0.99 0 0.65 0 0.72 O 0.81

Answer 1

Solution :

Given that,

mean = $\mu$ = 70

standard deviation = $\sigma$ = 1.6

n=16

$\mu$_{$\bar x$} = 70

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 1.6 / $\sqrt$ 16=0.4

= P(69< $\bar x$    <71 ) = P[(69 - 70) /0.4 < ( $\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ $\bar x$ < (71 - 70) /0.4 )]

= P( -2.5< Z <2.5 )

= P(Z <2.5 ) - P(Z <-2.5 )

Using z table,  

=0.9938 -0.0062

=0.9876( rounded)

answer= 0.99