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Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=152, where 0≤t≤52. Step 1 of 2: What is the probability that you will wait at least 38 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.

Answer :

Answer:

0.269

Step-by-step explanation:

Data provided in the question:

Probability density function f(t) = [tex]\frac{1}{52}[/tex]

where,  0 ≤ t ≤ 52

Now,

The probability that we will wait at least 38 minutes = Probability we will wait more than 38 minutes

thus,

integrating the Probability density function from 38 minutes to maximum time 52 minutes

therefore,

P = [tex]\int\limits^{52}_{38} {f(t)} \, dx = \int\limits^{52}_{38} {\frac{1}{52}} \, dx[/tex]

or

P = [tex]\frac{1}{52}[t]_{38}^{52}[/tex]

or

P =  [tex]\frac{1}{52}[52-38]}[/tex]

or

P = 0.269

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