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KonstantinChe [14]
4 years ago
11

A lumber company is making boards that are 2533.0 millimeters tall. If the boards are too long they must be trimmed, and if the

boards are too short they cannot be used. A sample of 14 is made, and it is found that they have a mean of 2536.4 millimeters with a variance of 64.00. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?
Mathematics
1 answer:
Slav-nsk [51]4 years ago
7 0

Answer:

Step-by-step explanation:

n = sample size =14\\Mean = x bar = 2536.4 mm\\Var = s^2 = 64\\Std dev =s =8\\\\Population mean = 2533.0\\Mean difference = 2536.4-2533 = 3.4\\Std error of sample = 8/sqrt 14 =2.14\\Test statistic = (3.4)/2.14) = 1.59

Since sample size is small and population std dev is not known, t test should be used.

p value = 0.135849

Since p>0.05 we accept that samples have a mean equal to 2533mm

There is no sufficient evidence to support the claim that the boards are either too long or too short

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The company estimated that they would sell 500 caps during the football season. They actually sold 575. Find the percent error.
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Answer:  

13.1%

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The company estimated that there would be 500 a ps during the football season

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Therefore the percent error can be calculated as follows

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3 years ago
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a) 30%

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a) The probability that one random person will be able to speak English is equal to the percent of the population that speaks English. This is because, in the country, (number of favorable outcomes)/(number of total outcomes) = 30% = 0.3 = 3/10

b) The probability that at least one person speaks English is equal to 1 - (probability that none of them speak English). Of the 4 people, if N represents them not speaking English and Y represents them speaking English, here are a few possiblities:

NNNN

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and so on. However, there is only one possibility where none of them speak  English, and the opposite of "none" is "at least one". So, the probability thsat none of them speak English is P(A and B and C and D) = P(A)*P(B)*P(C)*P(D), where P(A) represents the probability that the first person doesn't speak English and so on. The probability that the first person doesn't speak  English = 1 - (probability that the first person speaks English) = 1 - 30% = 0.7. Therefore, the probability that all of them don't speak English is 0.7^4 = 0.2401 and the probability that at least 1 of them speak English is 1- 0.2401 .= 0.7599 = 75.99%

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