The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function -3 F(x) = (1 − kx¯³ for x > 40000 0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the constant k here and provide its natural logarithm to three decimal places. Natural logarithm of k: Part b) Calculate the mean salary given by the model. Part c) Find the proportion in the profession earning less than the mean, giving your answers as a fraction or to three decimal places. ☐
The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function -3 F(x) = (1 − kx¯³ for x > 40000 0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the constant k here and provide its natural logarithm to three decimal places. Natural logarithm of k: Part b) Calculate the mean salary given by the model. Part c) Find the proportion in the profession earning less than the mean, giving your answers as a fraction or to three decimal places. ☐
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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![The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function
-3
F(x) =
(1 − kx¯³ for x > 40000
0 otherwise,
for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals.
Part a)
Find the constant k here and provide its natural logarithm to three decimal places.
Natural logarithm of k:
Part b)
Calculate the mean salary given by the model.
Part c)
Find the proportion in the profession earning less than the mean, giving your answers as a fraction or to three decimal places.
☐](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d69634b-8a8a-4609-8704-3bdadaefe256%2F81bfc21b-3249-4d0c-b474-ea7d07da3106%2F01qqadp_processed.png&w=3840&q=75)
Transcribed Image Text:The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function
-3
F(x) =
(1 − kx¯³ for x > 40000
0 otherwise,
for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals.
Part a)
Find the constant k here and provide its natural logarithm to three decimal places.
Natural logarithm of k:
Part b)
Calculate the mean salary given by the model.
Part c)
Find the proportion in the profession earning less than the mean, giving your answers as a fraction or to three decimal places.
☐
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