Answer:
The number of permutations of the group of letters given (J, K, L, M, N, O and P) is 7! = 7 . 6 . 5 . 4 . 3 . 2 . 1 = 5,040.
Step-by-step explanation:
The number of permutations without repetition is the number of possible sequences that can occur if we take the letters one by one and is calculated with the factorial of the total number of letters in the group.
Before starting we have 7 possibilities, one for each letter. Once the first letter is chosen randomly, we will have 6 possibilities, after taking the third letter we will have 5 possibilities, and so on.
In total the total number of possibilities to obtain the 7 letters in a certain order are 7 by 6 by 5 by 4 by 3 by 2 by 1, sayed in other words factorial of 7 (7!). The result of the multiplication gives 5,040.
In short we can get the seven letters in 5,040 different sequences.
Answer:
1 out of 15
Step-by-step explanation:
Cylinders are lengthy and tall and beakers are short and fat
Part A:
Finding the probability of P(Z < -1.27), we refer to the z-table to the left of the distribution and we have
Therefore
Part B:
Doing the same process as above, however we also need to find the P(Z < 1.68)
Solving for P(-1.27 < Z < 1.68) we have
![\begin{gathered} P\mleft(-1.27Part C:Again we need to find first P(Z < 1.96) to the left of zSince this probability is of P(Z < 1.96) , solve for P(Z > 1.96) by[tex]\begin{gathered} P\mleft(Z>1.96\mright)=1-P\mleft(Z1.96)=1-0.97500 \\ \\ \text{Therefore,} \\ P(Z>1.96)=0.02500 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5Cmleft%28-1.27%3Cstrong%3EPart%20C%3A%3C%2Fstrong%3E%3Cp%3EAgain%20we%20need%20to%20find%20first%20P%28Z%20%3C%201.96%29%20to%20the%20left%20of%20z%3C%2Fp%3E%3Cp%3ESince%20this%20probability%20is%20of%20P%28Z%20%3C%201.96%29%20%2C%20solve%20for%20P%28Z%20%3E%201.96%29%20by%3C%2Fp%3E%5Btex%5D%5Cbegin%7Bgathered%7D%20P%5Cmleft%28Z%3E1.96%5Cmright%29%3D1-P%5Cmleft%28Z%3C1.96%5Cmright%29%20%5C%5C%20P%28Z%3E1.96%29%3D1-0.97500%20%5C%5C%20%20%5C%5C%20%5Ctext%7BTherefore%2C%7D%20%5C%5C%20P%28Z%3E1.96%29%3D0.02500%20%5Cend%7Bgathered%7D)
15 the answer is 15 60/4 is15 15*4=60 which is 4 times bigger
