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Two types of interiors A & B are designed for Honda Accord 2018 model. Assume that the total customer review score (out of 100) for these two interior designs is independent and normally distributed. The review score of part A has a mean of 55 and a standard deviation of 5. The review score of part B has a mean of 60 and a standard deviation of 10. What is the probability that the review score of design B minus review score of design A is greater than 5?

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rodolforodriguezr

Answer:

50%

Step-by-step explanation:

Distribution 1

Mean

[tex]\bf \bar x_1[/tex] = 55

Distribution 2

Mean

[tex]\bf \bar x_2[/tex] = 60

Distribution 2 - Distribution 1

Mean

[tex]\bf \bar x_2-\bar x_1=60-55=5[/tex]

What is the probability that the review score of design B minus review score of design A is greater than 5

In any normal distribution X, the probability that X is greater than its mean is 50% or 0.5, so the probability that the review score of design B minus review score of design A is greater than 5 is 50%  

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