Basic Statistics05 marksNumerical: normal distribution probabilityNormal distribution properties and applications
A set of final examination grades in Basic Statistics, is following normal distribution with mean of 73 and standard deviation of 8. a.) What is the probability of a student secured less than 93 marks? b.)What is the probability of a student secured marks between 65 and 89?
A set of final examination grades in Basic Statistics, is following normal distribution with mean of 73 and standard deviation of 8. a.) What is the probability of a student secured less than 93 marks? b.)What is the probability of a student secured marks between 65 and 89? [5]
- Mean $\mu = 73$ - Standard Deviation $\sigma = 8$ - Distribution: Normal Z-score formula: $Z = \dfrac{X - \mu}{\sigma}$ --- Calculate Z for $X = 93$: $$Z = \frac{93 - 73}{8} = \frac{20}{8} = 2.5$$ From the standard normal table: $$P(X < 93) = P(Z < 2.5) = 0.9938$$ Answer: $0.9938$ or $99.38%$ ...