Thank you for visiting After measuring the height of all the college students at a local university a researcher found the following Mean height 62 8 inches Standard deviation. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The z-score for a height of 5 feet 8 inches with a mean of 62.8 and standard deviation of 4.3 is 1.2093, indicating that the individual is taller than about 88% of the population.
Explanation:
The question involves two parts: a) Finding the z-score for a height of 5 feet 8 inches using the given mean and standard deviation and b) Determining whether this height is taller than 90% of the population by referring to a Normal Distribution table.
Firstly, convert 5 feet 8 inches to inches only, making it 68 inches. Now, to find the z-score, you use the formula: z = (X - μ) / σ, where X is the value (68 inches), μ is the mean(62.8 inches), and σ is the standard deviation(4.3 inches). Plugging these numbers in, we get: z = (68 - 62.8) / 4.3 = 1.2093.
Now, in relation to part b), this cannot be answered without the specific values in the table on slide 21. However, generally, a z-score of 1.2093 corresponds roughly to the 88th percentile in a standard normal distribution, which would mean this individual is taller than about 88% of the population, but not 90%.
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