Answer:
1 minute
Step-by-step explanation:
We can see that Lisa types 165 words in 3 mins.
So she types 55 words in 1 minute.
How did I work that out?
Well, all you really do is which is equal to
if you divide top and bottom by 3. Anything divided by 1 is itself.
Answer:
0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?
This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So
X = 160
By the Central Limit Theorem
has a pvalue of 0.7257
X = 150
has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled
Answer:
a)
And for this case we can rewrite the model like this:
If we integrate both sides we got:
If we use exponentials for both sides we got:
For this case and r = -0.16
So then our model would be given by:
Where t represent the number of hours
b)
Step-by-step explanation:
Part a
For this case we can assume the proportional model given by:
And for this case we can rewrite the model like this:
If we integrate both sides we got:
If we use exponentials for both sides we got:
For this case and r = -0.16
So then our model would be given by:
Where t represent the number of hours
Part b
For this case we can replace the value t=5 into the model and we got: