Question

A population of values has a normal distribution with μ=153.5μ=153.5 and σ=17.7σ=17.7. You intend to draw a random sample of size n=31n=31.

Find the probability that a single randomly selected value is less than 153.8.
P(X < 153.8) =

Find the probability that a sample of size n=31n=31 is randomly selected with a mean less than 153.8.
P(M < 153.8) =

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

Solution :

Given that ,

mean = = 153.5

standard deviation = = 17.7

P(x < 153.8) = P[(x - ) / < (153.8 - 153.5) / 17.7 ]

= P(z <0.017 )

Using z table,

= 0.5068

n = 31

=   = 153.5

= / n = 17.7/ 31 = 3.179

P(M < 153.8) = P((M - ) / < (153.8 - 153.5) / 3.179 )

= P(z < 0.094)

Using z table

= 0.5374