select the correct answer.\nthe distribution of the number of occurrences of the letter t on the pages of a…

select the correct answer.\nthe distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. if there are 500 pages in the book, which sentence most closely summarizes the data?\na. the letter t occurs less than 26 times on approximately 170 of these pages.\nb. the letter t occurs less than 26 times on approximately 15 of these pages.\nc. the letter t occurs more than 26 times on approximately 420 of these pages.\nd. the letter t occurs more than 26 times on approximately 80 of these pages.

select the correct answer.\nthe distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. if there are 500 pages in the book, which sentence most closely summarizes the data?\na. the letter t occurs less than 26 times on approximately 170 of these pages.\nb. the letter t occurs less than 26 times on approximately 15 of these pages.\nc. the letter t occurs more than 26 times on approximately 420 of these pages.\nd. the letter t occurs more than 26 times on approximately 80 of these pages.

Answer

Explanation:

Step1: Calcular el z - score

El z - score se calcula con la fórmula $z=\frac{x - \mu}{\sigma}$, donde $x = 26$, $\mu=44$ y $\sigma = 18$. Entonces $z=\frac{26 - 44}{18}=\frac{- 18}{18}=-1$.

Step2: Encontrar la probabilidad correspondiente al z - score

Buscando en la tabla normal estándar, la probabilidad de $z < - 1$ es de aproximadamente $0.1587$.

Step3: Calcular el número de páginas

Multiplicamos la probabilidad por el número total de páginas. $0.1587\times500 = 79.35\approx80$. Esto significa que la letra $t$ ocurre menos de 26 veces en aproximadamente 80 páginas, entonces ocurre más de 26 veces en $500 - 80=420$ páginas.

Answer:

C. The letter t occurs more than 26 times on approximately 420 of these pages.