Respuesta :
Answer:
Ninety-five percent of all students at private universities pay less than $27,366.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 20232, \sigma = 4350[/tex]
Ninety-five percent of all students at private universities pay less than what amount?
They will pay less than the 95th percentile, that is, less than X when Z = 1.64. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.64 = \frac{X - 20232}{4350}[/tex]
[tex]X - 20232 = 1.64*4350[/tex]
[tex]X = 27366[/tex]
Ninety-five percent of all students at private universities pay less than $27,366.
Answer:
Step-by-step explanation:
Since the cost to attend a private university in the United States, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = cost to attend a private university.
µ = mean cost
σ = standard deviation
From the information given,
µ = $20232
σ = 4350
The probability of Ninety-five percent of all students at private universities is 0.95. Looking at the normal distribution table, the z is score corresponding to 0.95 is 1.65
Therefore
1.645 = (x - 20232)/4350
Cross multiplying, it becomes
1.65 × 4350 = x - 20232
x = 7177.5 + 20232 = 27409.5
x = 27410 to the nearest whole number
