Question

A population of values has a normal distribution with μ = 53.9 and σ = 71.9 . You intend to draw a random sample of size n = 168 . Find the probability that a single randomly selected value is between 39.5 and 70. P(39.5 < X < 70) = Find the probability that a sample of size n = 168 is randomly selected with a mean between 39.5 and 70. P(39.5 < M < 70) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	53.9
std deviation   =σ=	71.900

probability that a single randomly selected value is between 39.5 and 70:

probability =

P(39.5<X<70)

=

P(-0.2<Z<0.22)=

0.5886-0.4206=

0.1680

2)

sample size       =n=	168
std error=σx̅=σ/√n=	5.5472

probability that a sample of size n = 168 is randomly selected with a mean between 39.5 and 70:

probability =

P(39.5<X<70)

=

P(-2.6<Z<2.9)=

0.9981-0.0047=

0.9934