Answer:

Step-by-step explanation:
From the information given:
A meteorologist who sampled 4 thunderstorms of the sample size n = 16
the average speed at which they traveled across a certain state was 16 miles per hour ; i.e Mean
= 16
The standard deviation
of the sample was 4.1 miles per hour
The objective is to find the 90% confidence interval of the mean.
To start with the degree of freedom df = n - 1
degree of freedom df = 4 - 1
degree of freedom df = 3
At 90 % Confidence interval C.I ; the level of significance will be ∝ = 1 - C.I
∝ = 1 - 0.90
∝ = 0.10
∝/2 = 0.10/2
∝/2 = 0.050
From the tables;
Now the t value when ∝/2 = 0.050 is 

The Margin of Error = 
The Margin of Error = 
The Margin of Error = 
The Margin of Error = 
The Margin of Error = 4.82365
The Margin of Error = 4.82
Finally; Assume the variable is normally distributed, the 90% confidence interval of the mean is;


