30 POINTSSS!!!!
2 answers:
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Answer:
Less than 3.6 years.
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.
Mean of 5.8 years, and standard deviation of 1.7 years.
This means that
The 10% of items with the shortest lifespan will last less than how many years?
Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.
Less than 3.6 years.
Answer:
We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:
And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:
And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.