Question

A population of values has a normal distribution with \mu=192.6 and \sigma=34.4.

Random variables
ANSWERED
asked 2021-02-25

A population of values has a normal distribution with \(\displaystyle\mu={192.6}\) and \(\displaystyle\sigma={34.4}\). You intend to draw a random sample of size \(\displaystyle{n}={173}\).
Find the probability that a sample of size \(\displaystyle{n}={173}\) is randomly selected with a mean less than 186.1.
\(\displaystyle{P}{\left({M}{<}{186.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Answers (1)

2021-02-26

Step 1
Given:
\(\displaystyle\mu={192.6}\),
\(\displaystyle\sigma={34.4}\),
\(\displaystyle{n}={173}\).
The Z-score follows standard normal distribution.
Step 2
\(\displaystyle{P}{\left[{X}{<}{186.1}\right]}={P}{\left[{\frac{{{X}-\mu}}{{{\frac{{\sigma}}{{\sqrt{{{n}}}}}}}}}{<}{\frac{{{186.1}-{192.6}}}{{{\frac{{{34.4}}}{{\sqrt{{{173}}}}}}}}}\right]}\)
\(\displaystyle={P}{\left[{Z}{<}-{2.49}\right]}={0.0066}\) (Use standard normal table)
The probability that a sample of size \(\displaystyle{n}={173}\) is randomly selected with a mean less than 186.1 is 0.0066.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2020-10-27

A population of values has a normal distribution with \(\displaystyle\mu={192.3}\) and \(\displaystyle\sigma={66.5}\). You intend to draw a random sample of size \(\displaystyle{n}={15}\).
Find the probability that a sample of size \(\displaystyle{n}={15}\) is randomly selected with a mean less than 185.4.
\(\displaystyle{P}{\left({M}{<}{185.4}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

asked 2021-03-18

A population of values has a normal distribution with \(\displaystyle\mu={133.5}\) and \(\displaystyle\sigma={5.2}\). You intend to draw a random sample of size \(\displaystyle{n}={230}\).
Find the probability that a single randomly selected value is between 133.6 and 134.1.
\(\displaystyle{P}{\left({133.6}{<}{X}{<}{134.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

asked 2021-01-05

A population of values has a normal distribution with \(\displaystyle\mu={99.6}\) and \(\displaystyle\sigma={35.1}\). You intend to draw a random sample of size \(\displaystyle{n}={84}\).
Find the probability that a sample of size \(\displaystyle{n}={84}\) is randomly selected with a mean between 98.5 and 100.7.
\(\displaystyle{P}{\left({98.5}{<}\overline{{{X}}}{<}{100.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

asked 2020-12-07

A population of values has a normal distribution with \(\displaystyle\mu={99.6}\) and \(\displaystyle\sigma={35.1}\). You intend to draw a random sample of size \(\displaystyle{n}={84}\).
Find the probability that a single randomly selected value is between 98.5 and 100.7.
\(\displaystyle{P}{\left({98.5}{<}{X}{<}{100.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

...