laura picks 7 apples. some apples are red and some are green. fewer than 4 of the apples are red. how many of lauras apples coul
2 answers:
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Answer:
a. k = 3
b. Cumulative distribution function X,
c. Probability when headway exceeds 2 seconds = 0.125
Probability when headway is between 2 and 3 seconds = 0.088
d. Mean value of headway = 1.5
Standard deviation of headway = 0.866
e. Probability that headway is within 1 standard deviation of the mean value = 0.9245
Step-by-step explanation:
From the information provided,
Let X be the time headway between two randomly selected consecutive cars (sec).
The known distribution of time headway is,
a. Value of k.
Since the distribution of X is a valid density function, the total area for density function is unity. That is,
So, the equation becomes,
b. For this problem, the cumulative distribution function is defined as :
Now,
Therefore the cumulative distribution function X is,
c. Probability when the headway exceeds 2 secs.
Using cdf in part b, the required probability is,
Probability when headway is between 2 seconds and 3 seconds
Using the cdf in part b, the required probability is,
≅ 0.088
d. Mean value of headway,
And,
The standard deviation of headway is,
≅ 0.866
e. Probability that headway is within 1 standard deviation of the mean value
From part b, F(x) = 0, if x ≤ 1
Answer:
Option D is correct.
Step-by-step explanation
Principal = $9250
rate of interest = 7% or 0.07
time = 5 years or 260 weeks
[ Since there are 52 weeks in a year . for 5 years it will be 5x52=260 weeks]
Applying the formula
Amount after t years =
where P = principal
r = rate % in decimals
n= number of times in a year
t = times ( in years)
plugging the values in the formula
Amount =
=
=
= 9250(1.418733588)
=$13123.29