I need help with question 2 both A and B **Problems: Open book (please show all work!)**1. A normal distribution has a mean of μ = 100 and standard deviation of σ = 10. Find the following probabilities: a. $ p(X < 120) = \underline{\hspace{3cm}} $ b. $ p(X > 85) = \underline{\hspace{3cm}} $ c. $ p(86 < X < 103) = \underline{\hspace{3cm}} $2. For a normal population with μ = 100 and σ = 15, a. What is the probability of obtaining a **sample mean greater than 103** for a sample of n = 25 scores? b. What is the probability of obtaining a **sample mean less than 93** for a sample of n = 9 scores?

Name: I need help with question 2 both A and B **Problems: Open book (please
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Description: I need help with question 2 both A and B **Problems: Open book (please show all work!)**1. A normal distribution has a mean of μ = 100 and standard deviation of σ = 10. Find the following probabilities: a. \( p(X < 120) = \underline{\hspace{3cm}} \

Draw the normal curve and shade the area to the right of z=1. Refer to Standard normal…

Answered: 2. For a nomal population with u = 100…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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I need help with question 2 both A and B

**Problems: Open book (please show all work!)**

1. A normal distribution has a mean of μ = 100 and standard deviation of σ = 10. Find the following probabilities:

a. $ p(X < 120) = \underline{\hspace{3cm}} $

b. $ p(X > 85) = \underline{\hspace{3cm}} $

c. $ p(86 < X < 103) = \underline{\hspace{3cm}} $

2. For a normal population with μ = 100 and σ = 15,

a. What is the probability of obtaining a **sample mean greater than 103** for a sample of n = 25 scores?

b. What is the probability of obtaining a **sample mean less than 93** for a sample of n = 9 scores?

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathrm{\mathbf{given:}\;\mu=100,\;\sigma=5}$

$\mathrm{\mathbf{formula:}\;Z=\frac{M-\mu}{\frac{\sigma }{\sqrt{n}}}}$

$\mathrm{{\color{Blue} \mathbf{a.}}\;P(sample \;mean \;greater\; than\; 103)=P(M>103)=?}$

$\mathrm{given:\;n=25}$

$\mathrm{=P\left ( \frac{M-\mu}{\frac{\sigma }{\sqrt{n}}}>\frac{103-100}{\frac{15}{\sqrt{25}}} \right )}$

$\mathrm{=P\left ( Z>1 \right )}$

Draw the normal curve and shade the area to the right of z=1.

$\mathrm{\mathrm{Note:\;P\left ( Z>a \right )=1-P(Z<a)}}$

$\mathrm{\mathrm{=1-P(Z<1)}}$

Refer to Standard normal table/Z-table to find the probability of z=1.
OR
Use excel formula "=NORM.S.DIST(1, TRUE)" to find the probability.

$\mathrm{\mathrm{=1-0.8413}}$

$\mathrm{\mathrm{=\mathbf{{\color{Red} 0.1587}}}}$

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