Question

A population of values has a normal distribution with p = 229.4 and a = 67.4. You intend to draw a random sample of size n = 16. Find the probability that a single randomly selected value is greater than 212.6. PUX > 212.6) - Find the probability that a sample of size n = 16 is randomly selected with a mean greater than 212.6. PIM > 212.6) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z.scores or 2-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that ,

a) P(x > 212.6) = 1 - p( x< 212.6)

=1- p P[(x - $\mu$) / $\sigma$ < (212.6 - 229.4) / 67.4]

=1- P(z < - 0.249)

= 1 - 0.4017

= 0.5983

b) $\mu$ _{$\bar x$} = 229.4

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 67.4 / $\sqrt$ 16 = 16.85

P($\bar x$ > 212.6) = 1 - P($\bar x$ < 212.6 )

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (212.6- 229.4) / 16.85]

= 1 - P(z < - 0.997)   

= 1 - 0.1594

= 0.8406