LightCastle, a Bangladeshi business management consultant, employs a l

Michael Dennis

Michael Dennis

Answered question

2021-11-28

LightCastle, a Bangladeshi business management consultant, employs a large number of data analysts to analyze the data in survey project. The time it takes for new data analysts to learn the analysis procedure is known to have a normal distribution with a mean of 101 minutes and a standard.
a. What is the probability that the new data analysts will take more than 123 minutes to learn the analysis procedure?
b. What is the probability that the new data analysts will take between 97 to 141 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 95.59% of new analysts?

Answer & Explanation

Rosemary McBride

Rosemary McBride

Beginner2021-11-29Added 10 answers

Step 1
Given, mean(μ)=101
standard deviation (σ)=18
bit a
Required probability is P(X>123)
=P(Xμσ>123μσ)
=P(Z>12310118)
=P(Z>1.22)
=0.1112 (from Z-table)
bit b
Required probability is P(97<X<141)
=P(97μσ<Xμσ<141μσ)
=P(9710118<Z<14110118)
=P(0.22<Z<2.22)
=P(Z<2.22)P(Z<0.22)
=0.98680.4129 (from Z-table)
=0.5739
bit c
given probability is P(Zz0)=0.9559
P(Zz0)=0.9559
z0=1.705 (from Z-table)
X10118=1.705
X=101+(18×1.705)
X=131.69

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?