The mean number of days that the Monarch Butterfly spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is approximately Normal. What is the z-score for an individual butterfly that spends 12.7 days in its larval stage? - 0.64 O 0.64 O 6.29 0.74 O 0.26
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Question:**
The mean number of days that the Monarch Butterfly spends in its larval stage is 14.1 days, with a standard deviation of 2.2 days. This distribution is approximately Normal. What is the z-score for an individual butterfly that spends 12.7 days in its larval stage?
**Options:**
- ○ -0.64
- ○ 0.64
- ○ 6.29
- ○ 0.74
- ○ 0.26
**Explanation:**
To find the z-score, use the formula:
\[ z = \frac{(X - \text{mean})}{\text{standard deviation}} \]
Where:
- \( X \) is the individual value (12.7 days),
- Mean is 14.1 days,
- Standard deviation is 2.2 days.
Plugging these values into the formula gives:
\[ z = \frac{(12.7 - 14.1)}{2.2} = \frac{-1.4}{2.2} \approx -0.64 \]
Thus, the z-score is approximately -0.64.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a0b52e1-0c2d-471d-b963-79f93dce8c45%2Faa5e7381-6e75-4720-b505-d0538c934f63%2Fizool7_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
