9/11 - 1/2 in it's simplest form
1 answer:
Answer:
7/22
Step-by-step explanation:
Step 1: <u>Define/explain.</u>
To subtract fractions with different denominators, you must first find the least common denominator (LCM).
You can do this by listing the multiples of each denominator.
Step 2: <u>Solve.</u>
11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
22 is the LCM.
Now, we change the fractions to where they both have denominators of 22.
**REMEMBER: WHICHEVER NUMBER YOU MULTIPLY THE DENOMINATOR BY, YOU MULTIPLY IT BY THE NUMERATOR AS WELL!!**
Now, subtract as normal.
Step 3: <u>Conclude.</u>
Therefore, 9/11 - 1/2 = 7/22.
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Answer:
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in.
This means that
The width of a door is normally distributed with a mean of 23.87 in and a standard deviation of 0.08 in.
This means that .
Find the probability that the width of the casing exceeds the width of the door by more than 0.25 in?
This is P(C - D > 0.25).
Distribution C - D:
The mean is:
The standard deviation is:
Probability:
This probability is 1 subtracted by the pvalue of Z when X = 0.25. So
has a pvalue of 0.7704
1 - 0.7704 = 0.2296
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.