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Shayleechase
14.09.2019 •
Mathematics
finn changes his mind and, from now on, decides to take the normal route to work everyday. on any given day, the time (in minutes) it takes finn to get to work is normally distributed with mean u = 35 and variance = 81 .
find the 33rd percentile of the time it takes finn to get to work on any given day. do not include any units in your answer.
recall from question 6 that on any given day, the time (in minutes) it takes finn to get to work is normally distributed with mean = 35 and variance =81. assume the time it takes him to get to work is independent from day to day.
over the next 2 days, find the probability that finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.
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Ответ:
The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.
There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.
Step-by-step explanation:
This can be solved by the the z-score formula:
On a normaly distributed set with mean
and standard deviation
, the z-score of a value X is given by:
Each z-score value has an equivalent p-value, that represents the percentile that the value X is:
The problem states that:
Mean = 35, so![\mu = 35](/tpl/images/0231/2627/8ab19.png)
Variance = 81. The standard deviation is the square root of the variance, so
.
Find the 33rd percentile of the time it takes Finn to get to work on any given day. Do not include any units in your answer.
Looking at the z-score table,
has a pvalue of 0.333. So what is the value of X when
.
The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.
Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.
So:
There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.
Ответ:
good hows youres
Step-by-step explanation: