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 interpret the given area of 0.0594 using the provided values, we need to follow the steps to find the relevant proportions and probabilities.
First, let's calculate the values required to interpret the area.
Backward 4 = 266 days
Zero with a tail = 16 days
1) Interpretation 1 - Proportion of Human Pregnancies:
a) The proportion of human pregnancies that lasts between x = 290 and x = 350 days is:
To find this proportion, we need to find the area under the normal curve between x = 290 and x = 350.
1. Subtract Backward 4 from x = 290 to get a z-score:
Z1 = (290 - 266) / 16
2. Subtract Backward 4 from x = 350 to get another z-score:
Z2 = (350 - 266) / 16
3. Look up the z-scores in a standard normal distribution table or use a calculator to find the corresponding proportions associated with Z1 and Z2.
The area between x = 290 and x = 350 is given by the difference of these two proportions:
Area = Proportion(Z2) - Proportion(Z1)
This area represents the proportion of human pregnancies that last between 290 and 350 days.
b) The proportion of human pregnancies that lasts less than x = 290 days or more than x = 350 days is:
This can be calculated by subtracting the area found in step 3 (Area = Proportion(Z2) - Proportion(Z1)) from 1.
2) Interpretation 2 - Probability of Human Pregnancies:
a) The probability that a randomly selected human pregnancy lasts between x = 290 and x = 350 days:
Using the same calculations as in step 1, we can find the z-scores Z1 and Z2.
The probability is then given by the area between these two z-scores:
Probability = Proportion(Z2) - Proportion(Z1)
b) The probability that a randomly selected human pregnancy lasts less than x = 290 days or more than x = 350 days:
Again, using the calculations from step 1, the probability can be found by subtracting the area between x = 290 and x = 350 from 1.
By following these steps, you can calculate the proportions and probabilities for the given area using the provided values of backward 4 and zero with a tail.