Question 1 Math

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Georgian Court University *

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Statistics

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Jan 9, 2024

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Question: In a class of 30 students, the heights of students follow a normal distribution with a mean of 160 cm and a standard deviation of 5 cm. What percentage of students in the class are shorter than 155 cm tall? A) 15.87% B) 34.13% C) 84.13% D) 97.72% Answer: To find the percentage of students shorter than 155 cm tall in a normal distribution, you can use the Z-score formula: = − � � �� Z = σX − μ Where: � X is the value (height) we're interested in (155 cm), � μ is the mean (160 cm), and � σ is the standard deviation (5 cm). Calculate the Z-score: =155−1605=−55=−1 � Z = 5155−160 = 5−5 =−1 Consulting a standard normal distribution table or using a calculator, the area to the left of =−1 � Z =−1 is approximately 15.87%. Therefore, the answer is A) 15.87%.
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