Question

1. a certain amusement park ride requires riders to be at least 48 inches tall. if the heights of children in a summer camp are normally distributed with mean 52 and standard deviation 2.5, how many of the 140 campers will be allowed on the ride? round to the nearest integer. 6. what z - score on the normal curve table has an area of 0.8849 to its left? 7. what z - score on the normal curve table has an area of 0.6998 to its right?

Explanation:

Step1: Calculate the z - score for height requirement

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 48$ (the minimum height), $\mu = 52$ (mean height) and $\sigma=2.5$ (standard deviation).
$z=\frac{48 - 52}{2.5}=\frac{- 4}{2.5}=-1.6$

Step2: Find the proportion of children allowed

We look up the area to the left of $z=-1.6$ in the standard normal table. The area to the left of $z = - 1.6$ is $0.0548$. The proportion of children allowed (area to the right of $z=-1.6$) is $1 - 0.0548 = 0.9452$.

Step3: Calculate the number of children allowed

We have a total of $n = 140$ children. The number of children allowed is $n\times0.9452=140\times0.9452 = 132.328$. Rounding to the nearest integer, we get 132.

Answer:

132