Answer to Question #180645 in Statistics and Probability for Joshua Cornfield

Question

The Alien Invasion Survival Test scores are normally distributed with a mean of 110 and a standard deviation of 31. READ QUESTIONS CAREFULLY.

David gets a score of 87. What percentage of people will score higher than him on the same test? 

Answer for part 1

%

Stephanie’s standard score (z) on the test is 2.3. What score did she get on the test? 

Answer for part 2

What percentage of test takers scored between 87 and 110 on the test? 

Answer for part 3

%

Answer 1

The Alien Invasion Survival Test scores are normally distributed with a mean of 110 and a standard deviation of 31. READ QUESTIONS CAREFULLY.

David gets a score of 87. What percentage of people will score higher than him on the same test? 

Stephanie’s standard score (z) on the test is 2.3. What score did she get on the test? 

What percentage of test takers scored between 87 and 110 on the test? 

We have that

$\mu = 110$

$\sigma=31$

1) $P(X>87) = 1-P(Z<87)=1-P(Z<\frac{x-\mu}{\sigma})=1-P(Z<\frac{87-110}{31})=1-P(Z<-0.74)=1-0.2296=0.7704$

2)

$Z = 2.3$

$Z=\frac{x-\mu}{\sigma}=2.3 \implies x=2.3\sigma+\mu = 2.3\cdot31+110 = 181.3$

3)

$P(87<X<110)$ :

$P(X<110) = 0.5$ because the mean is 110, thus P(X<mean) = 50%

$P(X>87) = 0.7704$ from part 1)

therefore $P(87<X<110)= 0.7704 - 0.5 = 0.2704$

Answer:

1) 77.04% of people will score higher than David on the same test.

2) Stephany has got 181.3 score on the test.

3) 27.04% of test takers scored between 87 and 110 on the test.