Suppose a simple random sample of size nequals45 is obtained from a population with muequals64 and sigmaequals14. (a) what must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? assuming the normal model can be used, describe the sampling distribution x overbar. (b) assuming the normal model can be used, determine p(x overbarless than68.1). (c) assuming the normal model can be used, determine p(x overbargreater than or equals66.3).

Step-by-step explanation:

Given that sample size = n=45

mu = 64 and sigma =14

a) Sample mean will follow a normal distribution irrespective of the original distributions provided

i) samples are randomly drawn

ii) samples represent the population

iii) Sample size is sufficiently large

b) Here we have sample std dev=

c)

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1