-3 + { 1 – 3[20 + 2(-6 – 7)]}
1 answer:
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Answer:
(a) The probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b) On average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.
Step-by-step explanation:
Let <em>X</em> = number of motherboards that pass the inspection.
The probability that a motherboards pass the inspection is P (X) = <em>p</em> = 0.85.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is,
(a)
Compute the probability that at least 13 of the next 15 motherboards pass inspection as follows:
P (X ≥ 13) = P (X= 13) + P (X = 14) + P (x = 15)
Thus, the probability that at least 13 of the next 15 motherboards pass inspection is 0.6042.
(b)
Computed the expected number of motherboards should be inspected until a motherboard that passes inspection is found as follows:
Thus, on average, 1.18 motherboards should be inspected until a motherboard that passes inspection is found.
Answer:
The height of the cliff CD is approximately 539.76 m
Step-by-step explanation:
The given parameters are;
The first angle of elevation with which the captain sees the person on the cliff = 61°
The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°
The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°
∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;
The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°
By sine rule, we have;
AB/(sin(a)) = BC/(sin(c))
Which gives;
92/(sin(8°)) = BC/(sin(61°))
BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m
BC ≈ 578.165 m
The height CD = BC × sin(69°)
∴ The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.
The height of the cliff CD ≈ 539.76 m.
