# Probability of Finger Ridge Counts

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In the study of fingerprints, an important quantitative characteristic is the total ridge count for the 10 fingers of the individual. Suppose that the total ridge counts of individuals in a certain population are approximately normally distributed with a mean of 140 and a standard deviation of 50.

Find the probability that an individual picked at random from this population will have a ridge count of 200 or more.

In a population of 10,000 people how many would you expect to have a ridge count of 200 or more?

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##### Solution Summary

In about 135 words, this solution provides a step by step explanation of how to approach this mathematical-based problem which requires the formulation of equations to solve for the ridge count in a specific population. All calculations are provided.

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a) Denote the total ridge counts of individuals in a certain population by X. Then X is a random variable and approximately normally distributed with a mean of 140 and a standard deviation of 50, namely, ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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