A safety light is designed so that the times between flashes are normally distributed with a mean of and a standard deviation of . a. Find the probability that an individual time is greater than s. b. Find the probability that the mean for randomly selected times is greater than 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?

Complete question is;

A safety light is designed so that the times between flashes are normally distributed with a mean of 2.50s and a standard deviation of 0.50s.

A. Find the probability that an individual time is greater than 3.00 s.

B. Find the probability that the mean for 70 randomly selected times is greater than 3.00 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?

A) 0.15866

B) 0.00000001

C) Result in part B is more important

Step-by-step explanation:

A) We are given;

Mean; μ = 2.5

Standard deviation; σ = 0.5

To find the probability that an individual time is greater than 3 seconds, we will find the z-score and then find the p-value.

z = (x¯ - μ)/σ

z = (3 - 2.5)/0.5

z = 1

From z-distribution table attached, at z = 1, p(z < 1) = 0.84134

But we are looking for P(z > 1), thus;

P(z > 1) = 1 - 0.84134

P(z > 1) = 0.15866

B) now 70 are randomly selected. Thus, the z-score will be gotten from;

z = (x¯ - μ)/(σ/√n)

z = (3 - 2.5)/(0.5/√70)

z ≈ 8.37

From online calculations, we have;

P(z < 8.37) = 0.99999999

But we need P(z > 8.37).

This is:

P(z > 8.37) = 1 - P(z < 8.37)

P(z > 8.37) = 1 - 0.99999999

P(z > 8.37) = 0.00000001

C) The result in part B is more relevant because it is dealing with a sample size of 70 as against individual one in result A.

b.-4 units

all you   do is count how many times you move

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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