Question

A population of values has a normal distribution with \mu=120.6 and \sigma=48.5. You intend to draw a random sample of size n=105. Find the probability that a single randomly selected value is greater than 114.9. P(X > 114.9) =? Write your answers as numbers accurate to 4 decimal places.

Random variables
ANSWERED
asked 2021-02-13
A population of values has a normal distribution with \(\displaystyle\mu={120.6}\) and \(\displaystyle\sigma={48.5}\). You intend to draw a random sample of size \(\displaystyle{n}={105}\).
Find the probability that a single randomly selected value is greater than 114.9.
\(\displaystyle{P}{\left({X}{>}{114.9}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Answers (1)

2021-02-14
Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with mean \(\displaystyle\mu={120.6}\) and a standard deviation \(\displaystyle\sigma={48.5}\). The sample size is 105.
Step 2
The probability that a single randomly selected value is greater than 114.9 is
\(\displaystyle{P}{\left({X}{>}{114.9}\right)}={P}{\left({\frac{{{X}-\mu}}{{\sigma}}}{>}{\frac{{{114.9}-{120.6}}}{{{48.5}}}}\right)}\)
\(\displaystyle={P}{\left({Z}\succ{0.118}\right)}\)
\(\displaystyle={1}-{P}{\left({Z}{<}-{0.118}\right)}\)</span>
\(\displaystyle={1}-{0.4530}={0.5470}{b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{U}{\sin{{g}}}\ {t}{h}{e}\ {e}{x}{c}{e}{l}\ {f}{u}{n}{c}{t}{i}{o}{n}\backslash={N}{O}{R}{M}.{D}{I}{S}{T}{\left(-{0.118},{0},{1},{T}{R}{U}{E}\right)}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

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 2020-10-25
A population of values has a normal distribution with \(\displaystyle\mu={120.6}\) and \(\displaystyle\sigma={48.5}\). You intend to draw a random sample of size \(\displaystyle{n}={105}\).
Find the probability that a sample of size \(\displaystyle{n}={105}\) is randomly selected with a mean greater than 114.9.
\(\displaystyle{P}{\left({M}{>}{114.9}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2020-10-18
A population of values has a normal distribution with \(\displaystyle\mu={239.5}\) and \(\displaystyle\sigma={32.7}\). You intend to draw a random sample of size \(\displaystyle{n}={139}\).
Find the probability that a single randomly selected value is greater than 235.9.
\(\displaystyle{P}{\left({X}{>}{235.9}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2020-11-02
A population of values has a normal distribution with \(\displaystyle\mu={49}\) and \(\displaystyle\sigma={79.5}\). You intend to draw a random sample of size \(\displaystyle{n}={84}\).
Find the probability that a single randomly selected value is greater than 72.4.
\(\displaystyle{P}{\left({X}{>}{72.4}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2021-02-16
A population of values has a normal distribution with \(\displaystyle\mu={182.5}\) and \(\displaystyle\sigma={49.4}\). You intend to draw a random sample of size \(\displaystyle{n}={15}\).
Find the probability that a single randomly selected value is greater than 169.7.
\(\displaystyle{P}{\left({X}{>}{169.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2021-01-27
A population of values has a normal distribution with \(\displaystyle\mu={154.5}\) and \(\displaystyle\sigma={96.1}\). You intend to draw a random sample of size \(\displaystyle{n}={134}\).
Find the probability that a single randomly selected value is greater than 167.
\(\displaystyle{P}{\left({X}{>}{167}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2020-10-23
A population of values has a normal distribution with \(\displaystyle\mu={116.3}\) and \(\displaystyle\sigma={27.5}\). You intend to draw a random sample of size \(\displaystyle{n}={249}\).
Find the probability that a single randomly selected value is greater than 117.3.
\(\displaystyle{P}{\left({X}{>}{117.3}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2021-02-24
A population of values has a normal distribution with \(\displaystyle\mu={73.1}\) and \(\displaystyle\sigma={28.1}\). You intend to draw a random sample of size \(\displaystyle{n}={131}\).
Find the probability that a single randomly selected value is greater than 69.7.
\(\displaystyle{P}{\left({X}{>}{69.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2020-11-05
A population of values has a normal distribution with \(\displaystyle\mu={129.7}\) and \(\displaystyle\sigma={7.7}\). You intend to draw a random sample of size \(\displaystyle{n}={10}\).
Find the probability that a single randomly selected value is less than 130.9.
\(\displaystyle{P}{\left({X}{<}{130.9}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.
asked 2021-02-13
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 single randomly selected value is less than 186.1.
\(\displaystyle{P}{\left({X}{<}{186.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

You might be interested in

...