The time (in number of days) until maturity of a certain variety of tomato plant

Question

The time (in number of days) until maturity of a certain variety of tomato plant is normally distributed with mean and standard deviation = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The four times, in days, are

63 69 62 66.

Find a 99% confidence interval for and interpret it. Round your bounds of the interval to one decimal place; report them by filling in the blanks of the interpretation statement below:

We are 99% confidence that the true mean time to maturity for this variety of tomato plant is between blank #1 and blank #2days.

Blank #3:

If I wanted the margin of error for the 99% confidence interval to be ± 1 day, I should select a simple random sample of size ? Follow the rules of rounding for sample size determination.

Explanation / Answer

here mean for above sample of 4 =65

for std error of mean =std deviation/(n)1/2 =1.2

and for 99% CI, z=2.5758

hence confidence interval =sample mean +/- z*Std error =59.8483 ; 70.1517

2) for margin of error =1

z=2.5758

hence sample size =(z*std deviation/E)2 =~39

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