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A sample has a mean of 30 and standard deviation of 5. Assuming the data is normally distributed?
what is the probability that a given observation will have a value between 25 and 35?
a. 50%
b. 68%
c. 95%
d. 99%
e. 100%
Please let me know what the answer is and also how do you derive it?
1 Answer
- PolygonLv 78 years agoFavorite Answer
A sample has a mean of 30 and standard deviation of 5. Assuming the data is normally distributed?
what is the probability that a given observation will have a value between 25 and 35?what is the probability that a given observation will have a value between 25 and 35?
Z Score = (observation - mean)/standard deviation
Note that the Z score tables only show positive values because the measurement is taken from the mean rather than zero. When the formula gives a negative number the negative sign only indicates that your observation is less than the mean.
Z1 score = (25 - 30)/5 = -1.0
Z2 score = (35 - 30)/5 = + 1.0
From Z tables Z1 (1.0) = Pr (0.3413)
Z2 (1.0) = Pr (034213
Pr between 20 and 35 = 0.3413 + 0.3413 = 0.6826
Answer..............b
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