Great Insurance company has collected the data regarding the duration

deliriwmfg

deliriwmfg

Answered question

2021-12-03

Great Insurance company has collected the data regarding the duration (how long it takes) to settle insurance claims. The data collected indicate that the duration follows a normal distribution with mean 28 days and standard deviation 8 days.
1. What proportion of the duration is between 20 and 40 days old?
2. What proportion of the duration is less than 30 days old?
3. What is the number of days in which 75% of all claims are above?

Answer & Explanation

hotcoal3z

hotcoal3z

Beginner2021-12-04Added 16 answers

Step 1
the PDF of normal distribution is =1/σ2πexu2/2σ2 standard normal distribution is a normal distribution with, mean of 0, standard deviation of 1 equation of the normal curve is (Z)=xusdN(0,1)
mean(u)=28
standard deviation (sd)=8
Step 2
(1) to find P(aZb)=F(b)F(a)
P(X<20)=20288
=88=1
=P(Z<1) from standard normal table
=0.1587
P(X<40)=40288
=128=1.5
=P(Z<1.5) from standard normal table
=0.9332
P(20<X<40)=0.93320.1587=0.7745
proportion of the duration is between 20 and 40 days old is 77.45%
Step 3
(2) P(X<30)=30288
=28=0.25
=P(Z<0.25) from standard normal table
=0.5987
proportion of the duration is less than 30 days old is 59.87%
(3) p(z>x)=0.75
value of z to the cumulative probability of 0.75 from normal table is -0.6745
p(xus.d>x288)=0.75
that is, (x288)=0.6745
x=0.67458+28=22.6041
the number of days in which 75% of all claims are above is at 22.623days

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