manny2822
05.06.2020 •
Mathematics
A population of values has a normal distribution with μ = 247 and σ = 62.2. You intend to draw a random sample of size n = 16. (a) Find the probability that a single randomly selected value is greater than 295.2. (b) Find the probability that a sample of size n= 16 is randomly selected with a mean greater than 295.2. Give 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.
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Ответ:
a)
And using the normal distribution table or excel we got:
b)
And we can use the normal standard table or excel in order to find the probability and we got:
Step-by-step explanation:
For this case we know that the random variable of interest is normally distributed with the following parameters:
Part a
We want to find this probability:
And we can use the z score formula given by:
Replacing we got:
And using the normal distribution table or excel we got:
Part b
We select a random sample of size n = 16 and we try to find this probability:
And we can use the z score formula given by:
And replacing we got:
And we can use the normal standard table or excel in order to find the probability and we got:
Ответ: