Toby goes on holiday to Geneva, Switzerland. In Geneva, Toby sees a watch costing 193.75 CHF (Swiss Francs). In Manchester, an i
dentical watch costs £145. Given that £1=1.55CHF a) In which city is the watch cheaper. b) By how much is it cheaper (in £) i need help on part b , pleeeeaseeee help;(
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Answer:
The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.
Step-by-step explanation:
Prior concepts
A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".
The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".
Let X denote the random variable of interest, and we identify its distribution:
Also, let signify the sample mean, whose distribution is:
In this case,
Solution to the problem
We seek this probability
Applying the Z-score formula to the probability results in:
To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.
The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.
The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.
The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
Thus, the total rate of salt flow, represented by in grams, is defined by the differential equation,
which is linear. Shift the term to the right side, then multiply both sides by
:
Next, integrate both sides and solve for :
Initially, the tank contains 5 g of salt at time , so we have
The duration required for the tank to contain 20 g of salt is , such that