Standard normal distribution problem

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SUMMARY

The discussion centers on calculating the probability that a highway department's salt supply will suffice for 50 days of snowfall, given a daily mean of 1.5 inches and a standard deviation of 0.3 inches. The calculation involves using the Central Limit Theorem to approximate the total snowfall over 50 days, resulting in a Z-score of 2.36. Participants emphasize the importance of clarifying assumptions about the distribution of daily snowfall when applying statistical methods. The numerical value of 2.36 is confirmed as a valid outcome for the probability calculation.

PREREQUISITES
  • Understanding of the Central Limit Theorem
  • Knowledge of Z-scores and standard normal distribution
  • Familiarity with basic statistics, including mean and standard deviation
  • Ability to perform calculations involving probability distributions
NEXT STEPS
  • Study the Central Limit Theorem in detail
  • Learn how to calculate Z-scores for different distributions
  • Explore the implications of assumptions in statistical modeling
  • Practice problems involving normal distribution and probability calculations
USEFUL FOR

Students in statistics courses, data analysts, and anyone involved in probability calculations related to real-world scenarios, such as weather forecasting and resource management.

EdmureTully
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Homework Statement



(Page 222 number 5) A highway department has enough salt to handle a total of 80 inches of snowfall. Suppose the daily amount of snow has a mean of 1.5 inches and a standard deviation of .3 inches.

Approximate the probability that the salt on hand will suffice for the next 50 days.
What assumption did you make in solving part (a)?
Do you think this assumption is justified? Explain briefly.


Homework Equations





The Attempt at a Solution



I did 1.5x50 and

sqrt(50(0.3)^2)

and got P(Z<2.36)
 
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(Page 222 number 5)
In which book?

I did 1.5x50 and

sqrt(50(0.3)^2)

and got P(Z<2.36)
Please don't throw in some numbers without any explanation. What did you assume about the distribution of snow in the next 50 days? What did you calculate, with which formula? Which result did you get?

The numerical value of 2.36 looks good.
 

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