Respuesta :
Answer:
a) 0.021362
b) 0.139996
c) 0.062008
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 3.3% = 0.033
Standard Deviation, σ = 4.6% = 0.046
We are given that the distribution of mutual funds is a bell shaped distribution that is a normal distribution.
a) We have to find the value of x such that the probability is 0.4.
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.033}{0.046})=0.4[/tex]
Calculation the value from standard normal z table, we have,
[tex]P( z< -0.253) = 0.4[/tex]
[tex]\displaystyle\frac{x - 0.033}{0.046} = -0.253\\x = 0.021362[/tex]
b) We have to find the value of x such that the probability is 0.99
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.033}{0.046})=0.99[/tex]
Calculation the value from standard normal z table, we have,
[tex]P( z< 2.326) = 0.99[/tex]
[tex]\displaystyle\frac{x - 0.033}{0.046} = 2.326\\x =0.139996[/tex]
c) IQR = [tex]Q_3- Q_1 = 75^{th}\text{Percentile} - 25^{th}\text{Percentile}[/tex]
We have to find the value of x such that the probability is 0.75
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.033}{0.046})=0.75[/tex]
Calculation the value from standard normal z table, we have,
[tex]P( z< 0.674) = 0.75[/tex]
[tex]\displaystyle\frac{x - 0.033}{0.046} = 0.674\\x =0.064004[/tex]
We have to find the value of x such that the probability is 0.25
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.033}{0.046})=0.25[/tex]
Calculation the value from standard normal z table, we have,
[tex]P( z< -0.674) = 0.25[/tex]
[tex]\displaystyle\frac{x - 0.033}{0.046} = -0.674\\x =0.001996[/tex]
IQR = [tex]0.064004 - 0.001996 = 0.062008[/tex]
