Z-score and Percentile Help please. Answer with explanation. Both circled numbers
1 answer:
I assume all these measures are normally distributed, in which case the median and mean are equal.
15a. because the normal distribution is symmetric about the mean, and so 50% of families have an income greater than the average.
15b. by definition of percentile. The 90th percentile is $178,500, so the top 10% of families earn more than this.
15c. Because it's continuous, this distribution has the property . The top 10% earn more than $178,500, so the remaining 90% earn less. 50% of families earn more than the average, so 50% of families earn less than the average. Then
so 40% of families earn between the median and 90th percentile.
16a. or 75% because the first quartile is $570, meaning 25% of renters pay less than this amount.
16b. or 50% by the same reasoning used in (15a).
16c. or 25% by the same reasoning as in (15c).
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Answer: The chance here to win is 50%.
Step-by-step explanation: You are taking a chance on a spinner with 20 outcomes. So, we will be considering natural numbers from 1 to 20.
And also, you will a prize if you land on an even number, so we will calculate the probability of getting an even number.
From 1 to 20, there are 10 odd numbers and 10 even numbers out of total 20 numbers.
Let us define the following events -
A = event of getting an even number
and
B = event of getting an odd number.
So, n(A) = 10 and n(B) = 10.
So, the probability of getting an even number is given by
Thus, the required chance of winning a prize is 50%.
Answer:
1)
the mean rate of return is 17 %
the standard deviation of return is 17.06055
2)
the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325
Step-by-step explanation:
Given the data in the question;
1)
For the portfolio, the mean return and standard deviation are computed as follows;
Mean = Return = 0.65 × 10 + 0.35 × 30
= 6.5 + 10.5
= 17 %
Therefore, the mean rate of return is 17 %
Standard deviation will be;
σp = √( 0.65² × 15² + 0.35² × 40² )
= √( 0.4225 × 225 + 0.1225 × 1600 )
= √( 95.0625 + 196 )
= √291.0625
= 17.06055
Therefore, the standard deviation of return is 17.06055
2)
probability that Marvin's portfolio will make at least 20% over the next 12 months.
P( X > 20 )
we convert to a standard normal variable;
Z = )
Z = 0.17
from z table, p-value is;
p( X < 20 ) = 0.5675
P( X > 20 ) 1 - 0.5675 = 0.4325
Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325