Isa Trevino

2020-10-28

A population of values has a normal distribution with

Find the probability that a single randomly selected value is less than 226.9.

Write your answers as numbers accurate to 4 decimal places.

izboknil3

Skilled2020-10-29Added 99 answers

The probability that a single randomly selected value is less than 226.9 is,

$P\left(X<226.9\right)=P\left(\frac{X-\mu}{\sigma}<\frac{226.9-200}{31.9}\right)$

$=P\left(z<\frac{26.9}{31.9}\right)$

$=P\left(z<0.843\right)$

The probability of z less than 0.843 can be obtained using the excel formula “=NORM.S.DIST(0.843,TRUE)”. The probability value is 0.8004.

The required probability value is,

$P\left(X<226.9\right)=P\left(z<0.843\right)=0.8004$

Thus, the probability that a single randomly selected value is less than 226.9 is 0.8004.

Jeffrey Jordon

Expert2021-11-14Added 2575 answers

Answer is given below (on video)