Exam 7: Continuous Probability Distributions

A team of marine researchers is investigating ocean life that lives in the Hadalpelagic Zone (more than 6000 m beneath the surface).In this zone it is believed that the average depth at which the strange creatures that live here dwell is 7000 m, with a standard deviation of 200 m.If the distribution of depths is normal, 1.07% of the life in this zone lives above:

Spinal fusion surgery has become a popular and effective option for patients suffering from nerve pain caused by irregularities in the spinal disks.The effectiveness of the surgery varies from patient to patient.If the pain improvement post-surgery follows a normal distribution with a mean improvement of 2.25 and a standard deviation of 1.2, what is the probability that a randomly selected patient who undergoes fusion experiences a pain improvement between 0 and 2?

If a random variable X is normally distributed with mean μ = 0.45 and standard deviation σ = 0.40, then what is P(X ≥ 0.75)?

For any continuous random variable X, if a is any real fixed number, then P(X ≥ a) is always:

The memoryless property of the exponential distribution describes the fact that: