Question

According to the U.S. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. Eleven days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was x̄ = 8.3 million. Assume the distribution of the number of lightning strikes per day is normal with σ = 0.32 million. Please use 4 decimal places for all critical values.

(1 pt.) a) What assumptions are required so that you can construct a confidence interval for the mean number of lightning strikes per day?

(0.5 pts.) b) Find a 99% confidence interval for the mean number of lightning strikes per day.

(1 pt.) c) Interpret your answer in part b).

(0.5 pt.) d) Determine the number of days that need to be sampled to ensure that the half-width of the interval in b) is at most 0.08 million. Assume a confidence level of 99%.

Answer 1

a)   assumptions are as follows

sample should be simple random sample.

sampling distribution is normally distributed.

population standard deviation (σ) should be known.

b) C= 99%,  x̄ = 8.3, σ = 0.32, n= 11

formula for confidence interval is

where Zc is the Z critical value for C= 99%

8.0515 <    < 8.5485

Confidence interval is (8.0515 to 8.5485)

c) Interpretation:

Therefore we are 90% confident that the true mean number of lightning strikes

per day lies between 8.0515 to 8.5485

d)

E =0.08,

n = 106.5024

n= 107

number of days that need to be sampled =107