Question

8c )
what is the probability that a data value in a normal distribution is between a z - score of - 0.28 and a z - score of 0.64? round your
answer to the nearest tenth of a percent.

choice

a. 34.9%
b. 73.3%
c. 58.1%
d. 90.9%

question 9

9a )
suppose a normal distribution has a mean of 38 and a standard deviation of 2. what is the probability that a data value is between
37 and 41? round your answer to the nearest tenth of a percent.

choice

a. 83.5%
b. 56.5%
c. 77.5%
d. 62.5%

Explanation:

Step1: Encontrar la probabilidad para \(z = - 0.28\)

Usando la tabla normal estándar, \(P(Z < - 0.28)=0.3897\)

Step2: Encontrar la probabilidad para \(z = 0.64\)

Usando la tabla normal estándar, \(P(Z < 0.64)=0.7389\)

Step3: Calcular la probabilidad entre \(z=-0.28\) y \(z = 0.64\)

\(P(-0.28<Z<0.64)=P(Z < 0.64)-P(Z < - 0.28)\)
\(P(-0.28<Z<0.64)=0.7389 - 0.3897=0.3492\)

Step4: Convertir a porcentaje

\(0.3492\times100 = 34.92\%\approx34.9\%\)

Step1: Calcular \(z\) - score para \(x = 37\)

\(z=\frac{x-\mu}{\sigma}=\frac{37 - 38}{2}=-0.5\)

Step2: Calcular \(z\) - score para \(x = 41\)

\(z=\frac{x-\mu}{\sigma}=\frac{41 - 38}{2}=1.5\)

Step3: Encontrar \(P(Z < - 0.5)\)

Usando la tabla normal estándar, \(P(Z < - 0.5)=0.3085\)

Step4: Encontrar \(P(Z < 1.5)\)

Usando la tabla normal estándar, \(P(Z < 1.5)=0.9332\)

Step5: Calcular \(P(-0.5<Z<1.5)\)

\(P(-0.5<Z<1.5)=P(Z < 1.5)-P(Z < - 0.5)\)
\(P(-0.5<Z<1.5)=0.9332-0.3085 = 0.6247\)

Step6: Convertir a porcentaje

\(0.6247\times100=62.47\%\approx62.5\%\)

Answer:

A. 34.9%