A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution,what is the probability that an observation would be in this class?
A)0.4938
B)0.4772
C)0.0166
D)−0.0166

Question

Quizplus · Accepted Answer

To find the probability that an observation falls within the class limits of 50 to 60 in a normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 20, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$. For X = 50, $Z = \frac{50 - 100}{20} = -2.5$, and for X = 60, $Z = \frac{60 - 100}{20} = -2$. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities corresponding to Z = -2.5 and Z = -2, and then subtract the smaller probability from the larger one. This difference gives the probability of an observation falling between these two Z-scores, which is approximately 0.0166.

A Frequency Distribution Has a Mean of 100 and a Standard