Given two functions are
f(x) = 2 cos(x)
g(x) = 3 sin(x+ )
We know that the maximum value of cos x and sin x is always 1
y= maximum of cos = 1
y= maximum of sin =1
f(x) = 2 cos(x)
y= 2 (max of cos) = 2(1) = 2
g(x) = 3 sin(x+ )
y= 3 (max of sin) = 3(1) = 3
g(x) = 3 sin(x+ ) has the maximum value.
The probability that the aircraft is overloaded is 97.98%, which means the pilot should take the action.
In a Normal distribution with mean ц and standard deviation σ, the z-score of a measure x is given by:
Z = X-ц / σ
· It measures how many standard deviations the measure is from the mean.
· After finding Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
· By the Central Limit Theorem, the sampling distribution of sample means of the size n has standard deviation σ
σ = σ /
σ is standard deviation
n is the sample size.
Given that the mean and the standard deviation of the population is 176.1 lb and 35.4 respectively.
⇒ ц = 176.1 and σ = 35.4
For a sample of 43 passengers, we have
n = 43
σ =
σ = 5.398
Z = X-ц / σ
Z =
Z = -2.05 has p- value of 0.9798
The probability that the aircraft is loaded is
1 - p-value of Z
1 - 0.0202 = 0.9798
The probability that the aircraft is overloaded is 97.98%
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