Hi, This is a question about the random variable, could you please explain and s

Question

Hi,

This is a question about the random variable, could you please explain and solve this problem, thank you.

PS: The red text is the answer

Task: Confidence Intervals for a Normal Random Variable Each numerical entry must be accurate to the nearest 0.001 Given the normal random variable Z 4.4, 3.5 a. the 90% symmetric about the mean confidence interval has lower bound L and upper bound U F The datum 4.5755 (pic one) in the interval. k b. the 85% one-sided to the left confidence interval has upper bound U F The datum 0.7653 (pick one) in the interval c. the 90% one-sided to the right confidence interval has lower bound L The datum 3.3308 (pic one) n the interval. k CHECK a. L 1.3570, and U 10.1570 The datum 4.5755 is in the interval. b. U 8.0275 The datum 0.7653 is in the interval. c. L 0.0854 The datum 3.3308 is in the interval.

Explanation / Answer

here for normal distribuiton parameter mean=4.4

and std deviation=3.5

a)for 90% confidence interval , value of z score =1.645

hence lower bound =mean -z*std deviation =-1.3570

upper bound =mean +z*std deviation =10.1570

as 4.5755 lies in above interval; the datum 4.5755 is in the interval

b) for 85% one side bound ; z=1.0364

upper bound =mean +z*std deviation =8.0275

as -0.7653 is below 8.0275 ;

datum -0.7653 is in the interval

c) for 90% one sided bound, zscore =1.2816

hence lower bound =mean -z*std deviation =-0.0854

as datum 3.3308 is above that value, it is in the interval

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