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QuestionWhat is the probability of getting a number between 0.57 and 0.85 from a uniform distribution between 0 and 1? a. 15%15 \% b. 28%28 \% c. 32%32 \% d. 57%57 \%

Studdy Solution

STEP 1

Assumptions1. The random number generator produces uniformly distributed values between0 and1. . We are looking for the probability of obtaining a number between0.57 and0.85.

STEP 2

In a uniform distribution, the probability of an event occurring is equal to the length of the interval over which the event is defined. So, we can calculate the probability by taking the difference between the upper and lower bounds of the interval.
Probability=Upper bound−Lower boundProbability = Upper\, bound - Lower\, bound

STEP 3

Now, plug in the given values for the upper and lower bounds to calculate the probability.
Probability=0.85−0.57Probability =0.85 -0.57

STEP 4

Calculate the probability.
Probability=0.85−0.57=0.28Probability =0.85 -0.57 =0.28

STEP 5

The probability is a decimal value. To convert it to a percentage, multiply by100.
Probability (%)=Probabilitytimes100Probability\, (\%) = Probability \\times100

STEP 6

Plug in the calculated probability to convert it to a percentage.
Probability (%)=0.28times100Probability\, (\%) =0.28 \\times100

STEP 7

Calculate the probability percentage.
Probability (%)=0.28times100=28%Probability\, (\%) =0.28 \\times100 =28\%The probability of obtaining a number between0.57 and0.85 is28%.

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