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SOVA2 [1]
3 years ago
9

N general 20% of all students are left handed. a class of size 20 meets in a room with 5 left handed and 18 right handed chairs.

find the probability that each student will have a chair to their needs?
Mathematics
2 answers:
beks73 [17]3 years ago
8 0
All students will have a chair to their needs. So a 100% probability.
qaws [65]3 years ago
8 0

Answer:

The probability that each student will have a chair to their needs is P=0.6698.

Step-by-step explanation:

If 20 % of all students are left handed (LHS) and the class size is 20, there will be 4 left handed students and 16 right handed or ambidextrous (RHS). Then there are 5 left handed chairs (LHC) and 18 right handed (RHC), so there are 23 chairs. Now, you have to estimate the proportion for LHS, RHS, LHC and RHC.

P(LHS) = 4/20 ⇒ 0.2.

P(RHS) = 16/20 = 0.8.

P(LHC) = 5/23 = 0.217.

P(RHC) = 18/23 = 0.783.

Then to find the probability that each student will have a chair to their needs, we have to multiply P(LHS)xP(LHC) and P(RHS)xP(RHC) and sum.

⇒P(LHS)xP(LHC) + P(RHS)xP(RHC) = (0.2 x 0.217) + (0.8 x 0.783)

⇒ P(LHS)xP(LHC) + P(RHS)xP(RHC) = 0.6698.

Summarizing, the probability that each student will have a chair to their needs, is 0.6698.

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Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 pvalue, we get the probability that the value of the measure is greater than X.

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a) The percentage of heights less than 150 centimeters

We have to find the pvalue of Z when X = 150. So

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b) The percentage of heights between 160 centimeters and 180 centimeters

We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.

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Z = -0.25

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0.9878 - 0.4013 = 0.5865

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