Question

A population of values has a normal distribution with μ=243.5 and σ=64.4. A random sample of size n=174

is drawn.

1. Find the probability that a single randomly selected value is less than 257.7. Round your answer to four decimal places.
   P(X<257.7)=
2. Find the probability that a sample of size n=174 is randomly selected with a mean less than 257.7. Round your answer to four decimal places.
   P(M<257.7)=

Answer 1

Solution :

Given that ,

mean =   = 243.5

standard deviation = = 64.4   

P(X< 257.7) = P[(X- ) / < (257.7 -243.5) / 64.4]

= P(z <0.22 )

Using z table

= 0.5871

probability=0.5871

(B)

n = 174

= 243.5

=  / n = 64.4/ 174=4.8822

P( <257.7 ) = P[( - ) / < (257.7-243.5 ) / 4.8822]

= P(z 2.91< )

Using z table  

= 0.9982   

probability= 0.9982