For what values of x will this function be defined?
1 answer:
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Answer:
a) 0.1091
b) 0.9994
c) 0.5886
Step-by-step explanation:
X = the number of fish out of 20 that die after 24 hours
x = 0, 1, 2, . . . , 20
X~ Binomial (n= 20, p =0.20)
P(14 survive) = P(X = 6)
= =0.1091
Similarly we can find out
P(at least 10 survive) = P( X <= 10 ) = (Using technology) = 0.9994
P(at most 16 will survive) = P(X <= 16) = (Using technology) = 0.5886
Answer:
a) 0.7063; b) 0.0228; c) 0.2709
Step-by-step explanation:
We use z scores for these problems. The formula for a z sore is
For part a,
We want P(5 ≤ X ≤ 11):
z = (5-9.6)/2.3 = -4.6/2.3 = -2
z = (11-9.6)/2.3 = 1.4/2.3 = 0.61
The area under the curve to the left of z = -2 is 0.0228. The area under the curve to the left of z = 0.61 is 0.7291. This makes the area between them
0.7291 - 0.0228 = 0.7063
For part b,
We want P(X ≤ 5):
z = (5-9.6)/2.3 = -4.6/2.3 = -2
The area under the curve to the left of z = -2 is 0.0228.
For part c,
We want P(X > 11):
z = (11-9.6)/2.3 = 1.4/2.3 = 0.61
The area under the curve to the left of z = 0.61 is 0.7291. However, we want the area to the right; this means we subtract from 1:
1-0.7291 = 0.2709