Confidence Intervals: The new Twinkle bulb has mean life of

Hi wondering if anyone can tell me if I am on track with how I worked these problems? Thank you so much!

1) The new Twinkle bulb has a mean life of hours with a standard deviation of 35 hourshours. A random sample of 50 light bulbs is selected from inventory. The sample mean was found to be 550 hours.

a. Find the margin of error E for a 90% confidence interval. Round your answer to the nearest hundredths.
b. Construct a 90% confidence interval for the mean life

a. E=zc = 1.645 b.E=550-8.1=541.9 +E=550+8.1=558.1 Confidence interval =(549.1,558.1)

2) Mean of 115 and st. dev. of 10, If we want to be 90% certain we ar within 2 points of the true mean?

n=( C/E)2= =67.650625
rounded to nearest whole number=68

3) XBar is 190mg stand dev is 18.0 assume pop is norm dis. Find 95% conf interval?

a. N is less than 30 and ? is unknown and population is normally distributed so use T-Distribution

n=25, =190, s=18.0, c=0.95 d.f.=24
E=2.064 =7.4304 Rounded to the nearest tenth=7.4

b. find 95% conf inter for the mean assume pop is norm dis?

-E<?< +E
190-7.4<?<190+7.4
=182.6<?<197.4
So 95% Confidence Interval is (182.6,197.4)

Random sample of 100 and 75 worked. find the point estimate, and margin of error for 95% conf inter and construct 95% interval for pop proportion?
a.q=0.25 p=0.75
zc=1.96
E=0.107

Conf interval for this is (0.643, 0.857)