Answer:
Step-by-step explanation:
information given
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic
represent the p value for the test
Hypothesis to test
We want to test if the true mean is less than 12, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
We can replace in formula (1) the info given like this:
By normal curve symmetry
<span>from normal table </span>
<span>we have z = 1.15 , z = -1.15 </span>
<span>z = (x - mean) / sigma </span>
<span>1.15 = (x - 150) / 25 </span>
<span>x = 178.75 </span>
<span>z = (x - mean) / sigma </span>
<span>-1.15 = (x - 150) / 25 </span>
<span>x = 121.25 </span>
<span>interval is (121.25 , 178.75) </span>
<span>Pr((121.25-150)/25 < x < (178.75-150)/25) </span>
<span>is about 75%</span>
You have the right idea but the endpoint is at the wrong location. Instead, the green dot should go at -1. The shading is to the right. We use a closed filled in circle here (instead of an open hole) to tell the reader "include the endpoint". So -1 is part of the solution set.
In short, the graph consists of a closed filled in circle at -1 with shading to the right. This visually describes all values that are larger than -1, or equal to -1.
Hi! I believe your answer is <u>8,013.232</u>. The work is shown below. I hope this helps you! Good luck and have a great day. ❤️✨
