The figure to the right represents the normal curve with (backward 4)=266 days and zero with a tail =16 days the area between x=290 and x =350 is 0.0594 provide two interpretations of this area
Provide one Inter predation of the are using the given values
A) the proportion of human pregnancies that lasts between ? And days is?
The proportion of human pregnancies that lasts less than ? Or more than ? Is ?
Provide a second interpretation of the area using the given values
A) the probability that a randomly selected human pregnancy lasts between ? And ? Days is ?
B) the probability that a randomly selected human pregnancy lasts less than? Or more than? Days is?
To answer these questions, we need to use the normal distribution properties and understand how to calculate probabilities using z-scores.
First, let's interpret the given area of 0.0594 using the provided values.
Interpretation 1:
A) The proportion of human pregnancies that lasts between x = 290 and x = 350 days is 0.0594.
Interpretation 2:
A) The probability that a randomly selected human pregnancy lasts between x = 290 and x = 350 days is 0.0594.
B) The probability that a randomly selected human pregnancy lasts less than x = 290 days or more than x = 350 days is also 0.0594.
Now, let's calculate the missing values for the interpretations.
Interpretation 1:
A) To determine the proportion of human pregnancies that lasts between x = ? and x = ? days, we need to convert these values to z-scores. We can use the formula: z = (x - mean) / standard deviation.
In this case, "backward 4" represents the mean (μ) which is 266 days, and "zero with a tail" represents the standard deviation (σ) which is 16 days.
So, for example, if we want to know the proportion of human pregnancies that lasts between x = 290 and x = 350 days:
- For x = 290 days, the z-score would be (290 - 266) / 16 = 1.5.
- For x = 350 days, the z-score would be (350 - 266) / 16 = 5.25.
Once we have the z-scores, we can use a Z-table or a statistical software to find the proportion between these two z-scores. The value given in the question, 0.0594, can be interpreted as the proportion of human pregnancies that lasts between x = 290 and x = 350 days.
Interpretation 2:
A) To calculate the probability, we follow the same steps as in Interpretation 1 by converting the given x-values to z-scores. We can then use a Z-table or a statistical software to find the probability between these two z-scores.
For example, to find the probability that a randomly selected human pregnancy lasts between x = 290 and x = 350 days:
- Convert x = 290 days to a z-score: (290 - 266) / 16 = 1.5
- Convert x = 350 days to a z-score: (350 - 266) / 16 = 5.25
By consulting a Z-table or using statistical software, we can find the exact probability value.