Question

1. a certain amusement - park ride requires riders to be at least 48 inches tall. children on 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 0.6808 to its right?

Explanation:

Step1: Find z - score for area to the left

We know that if the area to the left is $A = 0.8849$, we look up this value in the standard - normal (z - score) table. The z - score corresponding to an area of $0.8849$ to the left is approximately $z_1=1.20$.

Step2: Find z - score for area to the right

If the area to the right is $A = 0.6808$, then the area to the left is $1 - 0.6808=0.3192$. Looking up $0.3192$ in the standard - normal table, the z - score is approximately $z_2=-0.47$.

Step3: Calculate number of campers allowed on the ride

We are given a normal distribution of campers with mean $\mu = 52$ and standard deviation $\sigma = 2.5$, and we want to find the number of campers $n$ such that $X\geq49$. First, we calculate the z - score for $X = 49$ using the formula $z=\frac{X-\mu}{\sigma}$. So, $z=\frac{49 - 52}{2.5}=\frac{-3}{2.5}=-1.2$.
The area to the left of $z=-1.2$ is $0.1151$ from the standard - normal table. The area to the right of $z=-1.2$ is $1 - 0.1151 = 0.8849$.
The number of campers allowed on the ride is $n = 0.8849\times140\approx124$.

Answer:

1. $z = 1.20$
2. $z=-0.47$
3. $124$