Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100
1 answer:
Answer:
16.59 inches
Step-by-step explanation:
Mean value = u = 14.5 inches
Standard deviation = = 0.9 in
We need to find the 99th percentile of the given distribution. This can be done by first finding the z value associated with 99th percentile and then using that value to calculate the exact value of hip breadth that lies at 99th percentile
From the z-table, the 99th percentile value is at a z-value of:
z = 2.326
This means 99% of the z-scores are below this value. Now we need to find the equivalent hip breadth for this z-score
The formula to calculate the z score is:
where, x is the hip breadth which is equivalent to this z-score.
Substituting the values we have:
Rounded to 2 decimal places, engineers should design the seats which can fit the hip breadth of upto 16.59 inches to accommodate the 99% of all males.
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Answer:
The probability is 0.0052
Step-by-step explanation:
Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:
P(A/B) = P(A∩B)/P(B)
The probability P(B) that at least three are aces is the sum of the following probabilities:
- The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
- There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:
So, the number of ways to select exactly 3 aces is:
Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725
Then, the probability P(B) that at least three are aces is:
On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:
P(A∩B) = 1/270,725
Finally, the probability P(A/B) that all four are aces given that at least three are aces is:
Answer:
Options (A), (B) and (C)
Step-by-step explanation:
In the given figure,
Length of side AD = 16 units
If this side is scaled by a factor = k
Then the length of the corresponding side will be = 16k
If 0 < k < 1,
Then length of the corresponding side will be less than 16.
[Example: If k =
Therefore, scaled side of the corresponding side of the quadrilateral = = 4]
That means length of corresponding sides may be 4, 6.5 and 12.
Options (A), (B) and (C) will be the answer.