Answer:
0.9544 or 95.44%
Step-by-step explanation:
Given: Mean= 37
Standard deviation= 6
x= 25 and 49.
Now, solving to find the percentage of daily phone calls numbering between 25 and 49.
[tex]Lets\ x_1= 25\ and\ x_2= 49[/tex]
first calculating the z-score for daily 25 phone calls.
Formula; [tex]z-score= \frac{x-mean}{standard\ deviation}[/tex]
z-score= [tex]\frac{25-37}{6}[/tex]
z-score= [tex]\frac{-12}{6} = -2[/tex]
∴ z-score for daily 25 phone call is -2.
Next, calculating the z-score for daily 49 phone calls.
z-score= [tex]\frac{49-37}{6}[/tex]
z-score= [tex]\frac{12}{6} = 2[/tex]
∴ z-score for daily 49 phone call is 2.
We can observe that there is change in z-score for 25 phone call and 49 phone call.
Lets use the normal distribution table to find the percentage of daily phone calls numbering between 25 and 49.
⇒ Percentage of daily phone calls numbering between 25 and 49= [tex](z-score\ x_2)- (z-score\ x_1)[/tex]
⇒ Percentage of daily phone calls numbering between 25 and 49= [tex](z-score\ 2)- (z-score\ -2)[/tex]
Using normal distribution table
⇒ Percentage of daily phone calls numbering between 25 and 49= [tex]0.9772 - 0.0228= 0.9544[/tex]
Hence, 0.9544 or 95.44% is the percentage of daily phone calls numbering between 25 and 49.
"0.9544 or 95.44% is the percentage of daily phone calls numbering between 25 and 49 To understand more information check below".
Given: Mean= 37
Standard deviation is = 6
Then, x is = 25 and 49.
Now, We are solving to find the percentage of daily phone calls numbering between 25 and 49.
Then, Lets x₁ = 25 and x₂ = 49
Now First we calculate the z-score for daily 25 phone calls.
Then we using a Formula; z - score = x - mean/ standard deviation
Then, z-score is = 25 - 37/6
z-score is = -12/6 = -2
∴ z-score for daily 25 phone calls is -2.
Now, calculate the z-score for daily 49 phone calls.
After that, z-score is = 49 - 37/6
Then, z-score is = 12/6 = 2
∴ z-score for daily 49 phone calls is 2.
Now, We can observe that there is a change in the z-score for 25 phone calls and 49 phone calls.
Let's use the normal distribution table to find the percentage of daily phone calls numbering between 25 and 49.
After that, ⇒ the Percentage of daily phone calls numbering between 25 and 49=
(z - scores x₂) - (z - score x₁)
Then, ⇒ the Percentage of daily phone calls numbering between 25 and 49=
(z - scores x₂) - (z - score - 2)
Using a normal distribution table
After that, ⇒ Percentage of daily phone calls numbering between 25 and 49=
Then, 0.9772 - 0.0228 is = 0.9544
Therefore, 0.9544 or 95.44% is the percentage of daily phone calls numbering between 25 and 49.
Find more information about Standard Deviation here:
https://brainly.com/question/22920224
