Respuesta :
Answer:
68
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 60
Standard deviation = 10
What percentage of days do you expect to have between 50 and 70 customers?
50 = 60 - 10
So 50 is one standard deviations below the mean.
70 = 60 + 10
So 70 is one standard deviation above the mean.
By the Empirical Rule, 68% of days do you expect to have between 50 and 70 customers. So the answer is 68
Answer:
Percentage of days we can expect to have between 50 and 70 customers = 68.3 .
Step-by-step explanation:
We are given that the number of customers at your company's store on a given day has a bell-shaped normal distribution with a mean of 60 and a standard deviation of 10 i.e.;
Mean, [tex]\mu[/tex] = 60 and Standard deviation, [tex]\sigma[/tex] = 10
Since, distribution is normal so;
Z score = [tex]\frac{X -\mu}{\sigma}[/tex] ~ N(0,1)
Let X = Number of customers
So, Probability(between 50 and 70) = P(50 <= X <= 70) = P(X<=70) - P(X<=50)
P(X <= 70) = P( [tex]\frac{X -\mu}{\sigma}[/tex] <= [tex]\frac{70 -60}{10}[/tex] ) = P(Z <= 1) = 0.84134
P(X <= 50) = P( [tex]\frac{X -\mu}{\sigma}[/tex] <= [tex]\frac{50 -60}{10}[/tex] ) = P(Z <= -1) = 1 - P(Z <= 1) = 1 - 0.84134 = 0.15866
So, Probability(between 50 and 70) = 0.84134 - 0.15866 = 0.68268 or 68.3%
Therefore, 68.3 percentage of days have customers between 50 and 70.
