Respuesta :
Answer:
15
Step-by-step explanation:
We know that heart rate measurements are normally distributed with mean μ=110. We have to find standard deviation whereas minimum and maximum value of data are 65 and 155 beats per min.
We know that by the empirical rule, 99.7% of value lies within 3 standard deviation from the mean. We can see that 99.7% covers approximately all the data and we can assume that all the data lies within 3 standard deviation. Now we check for each value whether the interval μ±3*σ contains minimum value 65 and maximum value 155 beats per min or not.
A. 5
μ±3*σ
110±3*5
110±15
(95,125)
B. 15
μ±3*σ
110±3*15
110±45
(65,155)
We can see that for standard deviation=15 , μ±3*σ contains minimum value=65 and maximum value=155.
C. 90
μ±3*σ
110±3*90
110±270
(-160,380)
Thus, the standard deviation of the distribution is most likely to be 15.
Using the normal distribution, it is found that the most likely standard deviation is of 15, option B.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It 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, which is the percentile of X.
In this problem:
- Mean of 110 hours, thus [tex]\mu = 110[/tex].
- Considering that approximately 100% of the measures are within 3 standard deviations of the mean, we consider than when X = 155, Z = 3, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]3 = \frac{155 - 110}{\sigma}[/tex]
[tex]3\sigma = 45[/tex]
[tex]\sigma = \frac{45}{3}[/tex]
[tex]\sigma = 15[/tex]
Thus standard deviation of 15, option B.
A similar problem is given at https://brainly.com/question/13452092
