Question

4. Let x be a random variable that represents the length of time it takes a student to complete a chemistry lab project. From long experience, it is known that x has a normal distribution with mean 1 3 .6 hours and standard deviation - 0.5. Find the chance that a student will take more than 4.5 hours to complete a lab project. 5. Using the information from #4, calculato the chance that the mean length of time for a random sample of 6 students is more than 3 hours.

Answer 1

4)
P(X >= 4.5) = P(z <= (4.5 - 3.6)/0.5)
= P(z >= 1.8)
= 1 - 0.9641
= 0.0359

5)
Here, μ = 3.6, σ = 0.5/sqrt(6) = 0.2041 and x = 3.
We need to compute P(X >= 3). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (3 - 3.6)/0.2041 = -2.94

Therefore,
P(X >= 3) = P(z <= (3 - 3.6)/0.2041)
= P(z >= -2.94)
= 1 - 0.0016
= 0.9984