LightCastle Partners, a Bangladeshi business management consultant, em

kenziebabyyy4e

kenziebabyyy4e

Answered question

2021-11-28

LightCastle Partners, a Bangladeshi business management consultant, employs a large number of data analysts to analyze the data in a survey project. The time it takes for new data analysts to learn the analysts procedure is known to have a normal distribution with a mean of 82 minutes and a standard deviation of 11 minutes.
a. What is the probability that the new data analysts will take more than 77 minutes to learn the analysis procedure?
b. What is the probability that the new data analysts will take between 54 to 85 minutes to learn the analysis procedure?
c. To maintain employee standars, LightCastle does not hire any analyst who fails to learn the process within a specified time. Therefore, what should be the specified time limit if they wish to retain at most 72.67% of new analysts?
? minutes

Answer & Explanation

Maked1954

Maked1954

Beginner2021-11-29Added 17 answers

Step 1
mean=μ=82 minutes
standard deviation =σ=11 minutes
z=xμσ,zN(0,1)
Step 2
(a) P(X>77)=P(xμσ>778211)
=P(z0.4545)
=P(z<0.4545)
=0.6753
(b) P(54<x<85)=P(548211<xμσ<858211)
=P(2.5454<z<0.2727)
=P(z<0.2727)P(z<2.5454)
=0.60750.0055
=0.602
(c) here P(x<x)=0.7267
we find x
P(xμσ<x8211)=0.7267
P(z<x8211)=0.7267
P(z<0.603)=0.7267
x8211=0.603x=82+0.603×11=88.633

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