Respuesta :
29.78% of customers will most likely probability be waiting between 4 and 9 minutes.
Explain the term z-score of the normal distribution?
- An observation's Z score indicates however many standard deviations it deviates from the mean.
- The standard normal distribution's mean is zero.
- Positive Z scores are those above the mean, while negative Z scores are those below the mean.
The formula for the z score is-
z = (x - μ)/σ
In which,
μ = mean of 10. 3 minutes
σ = standard deviation of 2. 7 minutes.
z score for the x = 4 minutes.
z = (4 - 10.3)/2.7
z = -2.33
z score for the x = 9 minutes.
z = (9 - 10.3)/2.7
z = -0.48
Thus,
Probability that the customer will have to wait between 4 and 9 minutes.
P(4 < x < 9) = P(-0.48 < z < -2.33)
Use z score table-
P(4 < x < 9) = 0.3085 - 0.0107
P(4 < x < 9) = 0.2978
P(4 < x < 9) = 29.78%
Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.
To know more about the z-score of the normal distribution, here
https://brainly.com/question/21781956
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