Suppose 3 neutrons are released by an atom of U-235 in the first stage of a fission chain reaction. Each of these neutrons has e
2 answers:
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Given Information:
Mean length of aluminum rods = μ = 10 cm
Standard deviation of length of aluminum rods = σ = 0.02 cm
Required Information:
a) P(9.98 < X < 10.02) = ?
b) P(9.90 < X < 10.1) = ?
Answer:
a) P(9.98 < X < 10.02) = 68.27%
b) P(9.90 < X < 10.1) = 100%
Explanation:
What is Normal Distribution?
Normal Distribution or also known as Gaussian Distribution, is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability
a) We want to find out the probability that the length of aluminum rods is between 9.98 and 10.02 cm.
The z-score corresponding to -1 is 0.15866 and 1 is 0.84134
Therefore, the probability that the length of aluminum rods is between 9.98 and 10.02 cm is 68.27%
b) We want to find out the probability that the length of aluminum rods is between 9.90 and 10.1 cm.
The z-score corresponding to -5 is 0 and 5 is 1
Therefore, the probability that the length of aluminum rods is between 9.90 and 10.1 cm is 100%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.0, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.00 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Explanation:
It is given that,
Bandwidth of a laser source,
(b) Let t is the time separation of sections of sections of the light wave that can still interfere. The time period is given by :
(a) Let h is the coherence length of the source. It is given by :
c is the speed of light
l = 0.0099 m
Hence, this is the required solution.