Question

A safety light is designed so that the times between flashes are normally distributed with a mean of

3.50 s and a standard deviation of 0.40 s.

a. Find the probability that an individual time is greater than 4.00s.

b. Find the probability that the mean for 60 randomly selected times is greater than 4.00 s.

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

1. The probability is approximately _____ (round to four decimal places as needed)
2. The probability is approximately_______ (round to four decimal places as needed)
3. Choose the correct answer

____(A) part (a) is more

A.___ Part​ (a) is more significant because the times of a single strobe is important.

B.____ Part​ (b) is more significant because the times of a single strobe is important

C.____ Part​ (a) is more significant because the average time for a sample is important.

D.___Part​ (b) is more significant because the average time for a sample is important

Answer 1

A safety light is designed so that the times between flashes are normally distributed with a

mean of 3.50 s and a standard deviation of 0.40 s.

a. Find the probability that an individual time is greater than 4.00s.

P ( x > 4.00 ) = P ( Z > 1.25 ) = 0.1056

The probability is approximately 0.1056

b. Find the probability that the mean for 60 randomly selected times is greater than 4.00 s.

n = 60

P ( x bar > 4.00 ) = P ( Z > 9.68 ) = 0.0000

The probability is approximately 0.0000

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

D.___Part​ (b) is more significant because the average time for a sample is important