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Answer: 15 meters

Step-by-step explanation:

Given the relation:

h(x) = −5(x+1)(x−3)

Where h is the height at time 'x' after diving

At the time of diving, time 'x' = 0, that her height just before making the dive

Therefore,

h(0) = - 5(0 + 1)(0 - 3)

h = - 5(1)(-3)

h = - 5 × - 3

h = 15

Therefore, h = 15 meters

Answer:

(a) P(X = 4) = 0.0189

(b) P(X 4) = 0.9919

(c) P(X 4) = 0.027

Step-by-step explanation:

We are given that the probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7 .

Since we have to find the probabilities for 1st successful alignments, so the probability distribution that we will use here is Geometric distribution.

<u>Geometric distribution</u> is used when we are interested in knowing the chances of our first success.

The probability distribution of geometric distribution is given by;

where, = number of trials

            k = first success = 1

            p = probability of getting success = 0.70

So, X ~ Geo(p = 0.7)

(a) Probability that the 1st successful alignment requires exactly 4 trials is given by = P(X = 4)

Here, = 4, p = 0.7 and k = 1

So, P(X = 4) = = = 0.0189

(b) Probability that the 1st successful alignment requires at most 4 trials is given = P(X 4)

 P(X 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)  

               =

               =

               = 0.7 + 0.21 + 0.063 + 0.0189 = 0.9919

(c) Probability that the 1st successful alignment requires at least 4 trials is given by = P(X 4)

    P(X 4) = 1 - P(X < 4) = 1 - P(X 3)

    P(X 4) = 1 - P(X = 1) - P(X = 2) - P(X = 3)

                  =  

                  =

                  = 1 - 0.7 - 0.21 - 0.063 = 0.027