Using the Empirical Rule, it is found that the desired probabilities are given as follows.
a) P(x > 158) = 0.16.
b) P(149 < x < 152) = 0.135.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Additionally, considering the symmetry of the normal distribution, 50% of the measures are below the mean and 50% are above.
Item a:
158 is one standard deviation above the mean, hence the probability is given by, considering that 32% of the measures are more than 1 standard deviation from the mean:
P(x > 158) = 0.5 x 0.32 = 0.16.
Item b:
Between one and two standard deviations below the mean, hence:
P(149 < x < 152) = 0.5 x (0.95 - 0.68) = 0.5 x 0.27 = 0.135.
More can be learned about the Empirical Rule at brainly.com/question/24537145
Answer:
y=Ae^(1.25t)
Step-by-step explanation:
From the expression y=Ae^kt
After two days of the experiment, y = 49 million, t=2
After four days of the experiment, y= 600.25 million, t=4
A is the amount of bacteria present at time zero and t is the time after the experiment (in days)
At t=2 and y =49
49=Ae^2k…………….. (1)
At t=4 and y = 600.25
600.25=Ae^4k………… (2)
Divide equation (2) by equation (1)
600.25/49=(Ae^4k)/(Ae^2k )
12.25=e^2k
Take natural log of both sides
ln(12.25) =2k
2.505 =2k
k=1.25
The exponential equation that models this situation is y=Ae^(1.25t)
Answer:
m
Step-by-step explanation:
The answer you seek is 15 and -4. 15*-4=-60 and 15-4=11.
Answer:
I think its the last one y=
x
Step-by-step explanation:
hope this helps
