A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included
2 answers:
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Answer:
(a1) The chance that the temperature rises by less than 20°C is 0.667.
(a2) The probability of the temperature increase falling between 20°C and 22°C is 0.133.
(b) The likelihood that the temperature increase could be hazardous at any moment is 0.467.
(c) The anticipated value of the temperature rise is 17.5°C.
Step-by-step explanation:
Let X denote the temperature increase.
The random variable X is distributed uniformly over the interval [10°C, 25°C].
The probability density function for X is shown here:
(a1)
The probability of the temperature increase being under 20°C can be calculated as follows:
Consequently, the chance that the temperature increase will be below 20°C is 0.667.
(a2)
The probability of the temperature rise being in the range from 20°C to 22°C is computed as follows:
This leads to the probability of the temperature increase being between 20°C and 22°C being 0.133.
(b)
To find the probability that the increase in temperature could be dangerous, we calculate:
This results in a probability of 0.467 that the temperature rise is potentially dangerous at any time.
(c)
The expected value of the uniform random variable X is determined as follows:
The expected value for the temperature increase computes to 17.5°C.