Probability of soft-drink machine

Click For Summary
SUMMARY

The discussion focuses on calculating the probability of a soft-drink machine dispensing between 191 ml and 209 ml per cup, given a mean of 200 ml and a standard deviation of 15 ml. The initial calculations using Z-scores resulted in a probability of 0.4714, but the correct probability, as referenced from the book "Areas under the normal curve," is 0.4514. The participant questions the necessity of continuity corrections in this context, concluding that they are not required unless specified for discrete amounts.

PREREQUISITES
  • Understanding of normal distribution and Z-scores
  • Familiarity with standard deviation and mean calculations
  • Knowledge of continuity correction in probability
  • Access to statistical tables or software for probability calculations
NEXT STEPS
  • Study the application of Z-scores in normal distribution problems
  • Learn about continuity correction and its relevance in probability distributions
  • Explore the use of statistical software for calculating probabilities
  • Review the concepts of mean and standard deviation in the context of real-world applications
USEFUL FOR

Students in statistics, data analysts, and professionals working with probability distributions who need to understand the nuances of calculating probabilities in continuous data scenarios.

superwolf
Messages
179
Reaction score
0
A soft-drink machine discharges an average of 200 ml per cup, with a standard deviation of 15 ml. What is the probability that a cup contains between 191 and 209 ml?


Attempt:

Z_1 = \frac{190.5-200}{15} = -0.63

Z_2 = \frac{209.5-200}{15} = 0.63

The table in my book "Areas under the normal curve", gives P = 0.7357-0.2643 = 0.4714

Correct answer (according to the same book): 0.4514

Are my continuity corrections wrong?
 
Physics news on Phys.org
I don't think that you need a continuity correction here, unless the problem specifies that the machine can only dispense discrete amounts.

(209 - 200)/15 = .6

P(Z < .6) = .7257
.7257 - (1-.7257) = .4514
 

Similar threads

Probability question on soft-drink machine
  • · Replies 6 ·
Replies
6
Views
3K
Solving Probability Question: Coffee Dispensed in ML per Cup
  • · Replies 1 ·
Replies
1
Views
4K
Probability and Statistics Questions
  • · Replies 1 ·
Replies
1
Views
5K
Mathematica This Week's Finds in Mathematical Physics (Week 231)
  • · Replies 5 ·
Replies
5
Views
3K
Mathematica This Week's Finds in Mathematical Physics (Week 231)
  • · Replies 5 ·
Replies
5
Views
3K