Answer:
The length of shadow is 69 foot.
Step-by-step explanation:
We are given a shadow of lighthouse.
Length of top of lighthouse to end of shadow is 90 ft.
Angle make at top of lighthouse is 50°
Distance from foot of lighthouse to end of shadow is x ft.
we need to find the length of shadow i,e x ft
Using trigonometry ration:
Hence, The length of shadow is 69 foot.
Answer:
0.0423 is the probability that the adult female has a height less than 61.3 inches.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 65.3 inches
Standard Deviation, σ = 2.32 inches
We are given that the distribution of adult female height is a bell shaped distribution that is a normal distribution.
Formula:
P(adult female has a height less than 61.3 inches)
Calculation the value from standard normal z table, we have,
0.0423 is the probability that the adult female has a height less than 61.3 inches.
Answer:
(a) 0.29412 .
(b) No, the events selecting company A and incurring in cost overruns are not independent.
Step-by-step explanation:
We are given that a certain federal agency employs three consulting firms (A, B and C) with probabilities 0.4, 0.35 and 0.25 respectively i.e.;
P(A) = 0.4 P(B) = 0.35 P(C) = 0.25
Also, From past experience it is known that the probability of cost overruns for the firms are 0.05, 0.03, and 0.15, respectively which means;
Let CO = Event of cost overruns
P(CO/A) = 0.05 - It means probability of cost overruns given the consulting firm involved was A.
Similarly, P(CO/B) = 0.03 P(CO/C) = 0.15
(a) Probability that the consulting firm involved is company A given a cost overrun is experienced by the company is given by, P(A/CO);
We will use Bayes' theorem here calculating the above probability ;
P(A/CO) =
= = 0.29412 .
(b) No, the events selecting company A and incurring in cost overruns are not independent because the cost overruns happens only when the consulting firm is involved and also the cost overruns will differ as we move towards another consulting firm so the chances of cost overruns will depend on the fact that which consulting firm has been involved.