A population of values has a normal distribution

Answered question

2022-04-09

A population of values has a normal distribution with μ=121.3 and σ=5.8. You intend to draw a random sample of size n=149.
Find the probability that a single randomly selected value is between 119.8 and 121.2.
P(119.8 < X < 121.2)

Find the probability that a sample of size n=149 is randomly selected with a mean between 119.8 and 121.2.
P(119.8 < M < 121.2)

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 & Explanation

nick1337

nick1337

Expert2022-06-08Added 777 answers

Use Excel formula:

=NORM.DIST(121.2,121.3,5.8,TRUE)-NORM.DIST(121.3,125.4,5.8,TRUE)

Answer: 0.2533066421

and

=NORM.DIST(121.1,121.3/SQRT(149),5.8,TRUE)-NORM.DIST(121.3,121.3/SQRT(149),5.8,TRUE)

Answer: 0

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