the grades of a science test are normally distributed. thanh finds that his grade on the test has a z…

the grades of a science test are normally distributed. thanh finds that his grade on the test has a z - score of -2.5. which statement must be true?\no thanhs grade is 2.5 standard deviations below the mean of the test grades.\no thanhs grade is 2.5 points below the mean of the test grades.\no thanhs grade is 2.5 standard deviations above the mean of the test grades.\no thanhs grade is 2.5 points above the mean of the test grades.

the grades of a science test are normally distributed. thanh finds that his grade on the test has a z - score of -2.5. which statement must be true?\no thanhs grade is 2.5 standard deviations below the mean of the test grades.\no thanhs grade is 2.5 points below the mean of the test grades.\no thanhs grade is 2.5 standard deviations above the mean of the test grades.\no thanhs grade is 2.5 points above the mean of the test grades.

Answer

Explanation:

Step1: Definición de puntuación z

La puntuación z en una distribución normal se define como $z=\frac{x - \mu}{\sigma}$, donde $x$ es el valor individual, $\mu$ es la media y $\sigma$ es la desviación estándar.

Step2: Interpretación de puntuación z negativa

Si $z=- 2.5$, significa que $x=\mu - 2.5\sigma$. Esto indica que el valor $x$ (la calificación de Thanh) está 2.5 desviaciones estándar por debajo de la media $\mu$.

Answer:

Thanh's grade is 2.5 standard deviations below the mean of the test grades.