Answer:
<u>Question 1:</u>
<u>(a) </u>P(x<60) = 0.9236
<u>(b) </u>P(x>16) = 0.9564
<u>(c) </u>P(16<x<60) = 0.88
<u>(d) </u>P (x>60) = 0.0764
<u />
<u>Question 2:</u>
<u>(a) </u>P(x<3) = 0.0668
<u>(b) </u>P(x>7) = 0.0062
<u>(c) </u>P(3<x<7) = 0.927
<u />
Step-by-step explanation:
<u>Question 1:</u>
x = no. of mg of porphyrin per deciliter of blood.
μ = 40
σ = 14
(a) We need to compute P(x<60). We need to find the z-score using the normal distribution formula:
z = (x - μ)/σ
P(x<60) = P((x - μ)/σ < (60 - 40)/14)
= P(z < 20/14)
= P(z<1.43)
Using the normal distribution probability table we can find the value of p at z=1.43.
P(z<1.43) = 0.9236
so, P(x<60) = 0.9236
(b) P(x>16) = P(z>(16-40)/14)
= P(z>-1.71)
= 1 - P(z<-1.71)
= 1 - 0.0436
P(x>16) = 0.9564
(c) P(16<x<60) = P((16-40)/14) < x < (60-40)/14)
= P(-1.71 < z < 1.43)
This probability can be calculated as: P(z<1.43) - P(z<-1.71)
P(16<x<60) = 0.9236 - 0.0436
P(16<x<60) = 0.88
(d) P(x>60) = 1 - P(x<60)
we have calculated P(x<60) in part (a) so,
P(x>60) = 1 - 0.9236
P (x>60) = 0.0764
<u>Question 2:</u>
μ = 4.5 mm
σ = 1.0 mm
In this question, we will again compute the z-scores and then find the probability from the normal distribution table.
(a) P(x<3) = P(z<(3-4.5)/1)
= P(z<-1.5)
P(x<3) = 0.0668
(b) P(x>7) = 1 - P(x<7)
= 1 - P(z<(7-4.5)/1)
= 1 - P(z<2.5)
= 1 - 0.9938
P(x>7) = 0.0062
(c) P(3<x<7) = P(x<7) - P(x<3)
we have computed both of these probabilities in parts (a) and (b) so,
P(3<x<7) = 0.9938 - 0.0668
P(3<x<7) = 0.927
. If the diameter is 8 the radius is 4, so filling in accordingly we have 
and 
which is 
and when you multiply in 3.14 you get that A = 401.92 or B above.