Q3) c & d Please answer only the c & d questions. Thank you! It is known from a new boulangerie in Cologne's Südstadt that the baguette weight (in grams) is normally distributed with an unknown...

Q3) c & d

Please answer only the c & d questions. Thank you!

It is known from a new boulangerie in Cologne's Südstadt that the baguette weight (in grams) is normally distributed with an unknown expected value µ and a theoretical standard deviation of 5.10 grams results in an average weight of 249.54 grams.
a) Determine a specific confidence interval for the expected value of the baguette weight at the confidence level 0.97 and enter the length of this interval.
b) How large must the sample be at least so that a confidence interval for the expected value of the baguette weight at the confidence level 0.97 has a length of at most
2.5 grams?

c)
How does the length of the confidence interval from sub-task a) change (with the same sample) if the confidence level is lowered to 0.92?

d)
It is also known that the weight of baguettes (in grams) from a second boulangerie in the village is also normally distributed, whereby both parameters µ and σ are unknown here.
For this boulangerie, a size 35 sample found an average baguette weight of 248.21 grams and a sample standard deviation of 6.24 grams. Also determine a specific confidence interval for the expected value
of the baguette weight of this second boulangerie, also here at the confidence level 0.97, and interpret the obtained confidence interval.