Answer:
b > 12.71
Step-by-step explanation:
Here in this question we have to solve the inequality equation given for b (An unknown variable}
Now, the equation is
⇒
We are taking the base of the log here is 10.
So, {Since
and
}
⇒ b > 12.71 (Approximate) (Answer)
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Explanation:
s = 32 = sample standard deviation
n = 40 = sample size
Despite not knowing the population standard deviation (sigma), we can still use the Z distribution because n > 30. When n is this large, the student T distribution is approximately the same (more or less) compared to the standard Z distribution. The Z distribution is nicer to work with.
At 90% confidence, the z critical value is roughly z = 1.645. This can be found using either a Z table or a calculator.
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We have these values:
Plug these values into the margin of error formula.
The margin of error is roughly 8.323
I rounded to 3 decimal places because z = 1.645 is rounded to 3 decimal places. If your teacher wants some other level of precision, then be sure to follow those instructions.