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Answer:
34.87% probability that all 5 have a wireless device
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they own a wireless device, or they do not. The probability of a student owning a wireless device is independent from other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
81% of students own a wireless device.
This means that
If 5 students are selected at random, what is the probability that all 5 have a wireless device?
This is P(X = 5) when n = 5. So
34.87% probability that all 5 have a wireless device
Answer:
(a). The mean speed is 760 m/s.
(b). The standard deviation for our normal model is 142.1 m/s.
(c). The unusual speed is 1127 m/s.
(d). The average molecule speed is 929.48 m/s.
Step-by-step explanation:
Given that,
Molecules in the air are moving with speeds based on the normal model.
Let x be the speed of the molecules.
(a). If half of the air molecules are moving faster than 760 m/s.
We can say speed of a molecules is normally distributed.
So, the mean, median and mode of this distribution is at least greater than 760 m/s.
(b). If exactly 95% of the molecules are moving with speeds between 475.8 m/s and 1044.2 m/s,
If the standard deviation is σ and the mean is μ,
We need to calculate the standard deviation for our normal model
Using empirical rule
...(I)
....(II)
Put the value of μ in equation (I)
(c). One molecule is found to be moving with a speed of 1127 m/s.
We know that,
1127 is the between 1126 and 1128.
Since, it is a continuous distribution,
We need to find the probability that speed is between this
Using excel function
We know that,
Any probability less than 0.05 is considered as unusual
So, 0.0002<0.05
So, 1127 will be considered as the unusual speed.
(d). If the temperature increase caused the z-score of a particle moving at 1100 m/s particle to drop to 1.2 after the temperature increase.
We need to calculate the average molecule speed
Using formula of average molecule speed
Put the value in to the formula
Hence, (a). The mean speed is 760 m/s.
(b). The standard deviation for our normal model is 142.1 m/s.
(c). The unusual speed is 1127 m/s.
(d). The average molecule speed is 929.48 m/s.