Question

elizabeth is getting married, and her budget only allows her to spend, at most, $750 on a wedding cake. she learns that the prices of wedding cakes follow a normal distribution, with a mean of $528 and a standard deviation of $155. what percentage of wedding cakes in this distribution cost more than $750?

91.92%
11.51%
8.08%
84.13%
9.68%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 750$, $\mu=528$, and $\sigma = 155$.
$z=\frac{750 - 528}{155}=\frac{222}{155}\approx1.43$

Step2: Find the cumulative probability

We use the standard normal distribution table (or z - table) to find $P(Z\leq1.43)$. Looking up 1.43 in the z - table, we get $P(Z\leq1.43)\approx0.9236$.

Step3: Calculate the probability of $Z > 1.43$

Since the total area under the normal curve is 1, $P(Z>1.43)=1 - P(Z\leq1.43)$.
$P(Z>1.43)=1 - 0.9236 = 0.0764\approx8.08\%$

Answer:

8.08%