Suppose the cumulative distribution function of the random variable X is Round your answers to 3 decimal places. Determine the following: a) b) c) d) Statistical Tables and Charts

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Full Question

Suppose the cumulative distribution function of the random variable X is F (x) = 0.25x + 0.4

For {0, x < - 1.6; - 1.6 ≤ x ≤ 2.4; 1, x ≥ 2.4}

(Round your answers to 3 decimal places) Determine the following:

1. P (X < 1.8)

2. P (X> - 1.5)

3. P (X < - 2)

Answer:

1. P (X<1.8) = 0.85

2. P (X> - 1.5) = 0.975

3. P (X < - 2) = 0

Step-by-step explanation:

1. Calculating P (X < 1.8);

Since, F (x) = 0.25x + 0.4

P (X<1.8) = 0.25 (1.8) + 0.4

P (X<1.8) = 0.85 or 85%

2. Calculating P (X> - 1.5)

Here

P (X> - 1.5) + P (X≤-1.5) = 1

P (X> - 1.5) = 1 - P (X≤-1.5)

Calculating P (X≤-1.5)

P (X≤-1.5) = 0.25 (-1.5) + 0.4

P (X≤-1.5) = 0.025

So,

P (X> - 1.5) = 1 - 0.025

P (X> - 1.5) = 0.975

3. Calculating P (X < - 2)

X < - 2 doesn't fall within the range of values given in (question) above.

So, P (X < - 2) = 0