Respuesta :
Answer:
0.0323 = 3.23%. Is unusual
Step-by-step explanation:
Using the normal distribution we can find z value with the mean and standard deviation as follows. x is the value we want to know its probability
z = (x - mean)/standard deviation
z = (5-8.54)/1.91
z = -1.85
Using z tables for normal distribution, for z = 1.85, we have an area under the curve of 0.9677. Since we want to know the probability for 5 minutes or less, we have to substract from
p = 1- 0.9677
p = 0.0323
An event with a probability less than 5% is considered unusual.
Answer:
The answer is 0.0918, it is not unusual.
Step-by-step explanation:
Given :
The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes
The standard deviation is 1.91
i.e. [tex]$\mu=8.54[/tex] minutes and [tex]$\sigma=1.91$[/tex] minutes.
Let [tex]x[/tex] denotes the length of time a person takes to decide which shoes to purchase.
Formula :
[tex]$z=\frac{x-\mu}{\sigma}$[/tex]
Then, the probability that a randomly selected individual
It will takes as less than 6 minutes to select a shoe purchase will be the [tex]$\mathrm{P}$[/tex] -value
Then
[tex]$=P(x<6)=P\left(\frac{x-\mu}{\sigma}<\frac{6-8.54}{1.91}\right)$[/tex]
[tex]$\approx P(z<1.33)=1-P(z<1.33) \quad[P(Z<-z)=1-P(Z<z)]$[/tex]
[tex]$=1-0.9082[\mathrm[/tex]By using [tex]$\mathrm{z}$[/tex] -value ][tex]=0.0918[/tex]
Thus, the required probability [tex]=0.0918[/tex]
Since, P-value [tex]$(0.0918)>0.05$[/tex], it means this outcome is not unusual.
[Note : When a outcome is unusual then the probability of its happening is less than or equal to [tex]0.05[/tex] ]
For more reference about probability,
brainly.com/question/11234923
