Answer: 457.3
Step-by-step explanation:
= 457.3
Nadia solved the equation 4x-4=20!4x=16 x=4what error did she make
2 answers:
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Answer:
a) 85.31%
b) 56 minutes
c) 17 days
d) 0.1721
Step-by-step explanation:
In order to make the calculations easier, let's <em>standardize the curve</em> by doing the change
where is the average trip-time and
the standard deviation and
P(X≤ t) is the probability that the trip takes less than t minutes.
a)
Here we are looking for the value of P(X>20).
For X=20 we have Z = (20-24)/3.8 = -1.05
So, we want the area under the standard normal curve for Z > -1.05
that we can compute either using a table or a computer and we find this area equals 0.8531
So, he arrives late to work 85.31% of the times.
(See picture 1 attached)
b)
In this case we are looking for a value t of time such that
P(X≥ t) = 20% = 0.2
So, we are seeking a value Z such that the area under the normal curve to the left of Z equals 0.2
By using a table or a computer we find Z = 0.842
(See picture 2 attached)
By inserting this value in the equation on standardization
So 20% of the longest trips takes 55.996 ≅ 56 minutes
c)
Since the average of days he arrives late is 85.31%, it is expected that in 20 work days he arrives late 85.31% of 20, which equals 17 days.
d)
Since the probability that he does not arrive late is 1-0.8531 = 0.1469 and the probability of arriving early is independent of the previous trip,
the probability of arriving early n days in a row is
0.1496*0.1496*...*0.1496 n times and
the probability of being early most than 10 trips in 20 days is
Answer:
a. 97.72% of the observations are less than 33
b. Approximately 977 observations are less than 33.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 25 and a standard deviation of 4.
This means that
a. Approximately what percentage of the observations are less than 33?
The proportion is the p-value of Z when X = 33. So
has a p-value of 0.9772
0.9772*100% = 97.72%
97.72% of the observations are less than 33.
b. Approximately how many observations are less than 33?
Out of 1000:
0.9772*1000 = 977.2
Approximately 977 observations are less than 33.