3 lines are shown. A line with points M, H, K intersects a line with points J, H, L at point H. A line extends from point H to p
1 answer:
You might be interested in
Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
Sample standard deviation:
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0.150
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample. So
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Lyra's speed of travel is 6.71 feet per seconds and Lyra's direction of travel is 27 degrees north of east
<h3>How to determine the speed of travel?</h3>The diagram that represents the scenario is added as an attachment.
Let x represents Lyra's speed of travel.
The value of x is calculated using the following Pythagoras theorem.
Evaluate the exponents
Evaluate the sum
Evaluate the exponent
x = 6.71
Hence, Lyra's speed of travel is 6.71 feet per seconds
<h3>How to determine the direction of travel?</h3>The direction (∅) is calculated using the following tangent ratio.
Evaluate the quotient
Take the arc tan of both sides
Evaluate
Hence, Lyra's direction of travel is 27 degrees north of east
Read more about speed and distance at:
#SPJ1
