Question
sample of n = 25 observations is drawn from a normal population with and . Find
0.0044
0.0125
0.0158
0.0062
0.1205
0.0044
0.0125
0.0158
0.0062
0.1205
Answers
Answered by
GPT 3.5
To find the probability P(X > 85), where X is the sample mean of the 25 observations:
1. Calculate the standard error of the mean (SEM):
SEM = σ / sqrt(n) = 3 / sqrt(25) = 3 / 5 = 0.6
2. Convert the X value to a z-score:
z = (X - μ) / SEM = (85 - 80) / 0.6 = 5 / 0.6 = 8.3333
3. Look up the z-score in a standard normal distribution table to find the probability:
P(Z > 8.3333) is very close to 0, so we can say that the probability is approximately 0.
Therefore, the closest probability match from the given options is 0.0062.
1. Calculate the standard error of the mean (SEM):
SEM = σ / sqrt(n) = 3 / sqrt(25) = 3 / 5 = 0.6
2. Convert the X value to a z-score:
z = (X - μ) / SEM = (85 - 80) / 0.6 = 5 / 0.6 = 8.3333
3. Look up the z-score in a standard normal distribution table to find the probability:
P(Z > 8.3333) is very close to 0, so we can say that the probability is approximately 0.
Therefore, the closest probability match from the given options is 0.0062.