G During an experiment, an aerospace engineering student measures a wind tunnel’s velocity N times. The student reports the following information, based on 90 % confidence, about the finite data set: mean velocity = 25.00 m/s, velocity standard deviation = 1.50 m/s, and uncertainty in velocity = 2.61 m/s. Determine (a) N, (b) the standard deviation of the means based upon this data set (in m/s), (c) the uncertainty, at 95 % confidence, in the estimate of the true mean value of the velocity (in m/s), and (d) the interval about the sample mean over which 50 % of the data in this set will be (in m/s).

a

b

The standard deviation is

c

The uncertainty at 95% is

d

The interval about the sample mean is  

Explanation:

From the question we are told that

       The confidence level is  %

       The mean velocity is  

       The velocity standard deviation is  

        The uncertainty of the velocity

Generally uncertainty can be represented mathematically as

Where   is the z-score of 0,05 = 1.645 from the z-table  

            Substituting value

The standard deviation of the mean is mathematically represented as

Substituting the values

The uncertainty for confidence level of 95% is mathematically represented as

   Where is the z value  of the 0.95 which is  1.96, this is obtained using the z-table

             Substituting values

The uncertainty for confidence level of 50 % is mathematically represented as          

     Where is the z value  of the 0.50 which is  0.69146, this is obtained using the z-table                  

           Substituting values

So the interval about the sample mean is      

what are the statements? x