MATH SOLVE

2 months ago

Q:
# A boat capsized and sank in a lake. Based on an assumption of a mean weight of 149 lb, the boat was rated to carry 70 passengers (so the load limit was 10 comma 430 lb). After the boat sank, the assumed mean weight for similar boats was changed from 149 lb to 173 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 35.8 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb. The probability is

Accepted Solution

A:

Answer:There is a 78.81% probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb.Step-by-step explanation:Problems of normally distributed samples can be solved using the z-score formula.In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by[tex]Z = \frac{X - \mu}{\sigma}[/tex]After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 177.2 lb and a standard deviation of 35.8 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb. Here we have that [tex]\mu = 177.2, \sigma = 35.8, X = 149[/tex]. We want to find the probality that the measure is greater than 149. So[tex]Z = \frac{X - \mu}{\sigma}[/tex][tex]Z = \frac{149 - 177.2}{35.8}[/tex][tex]Z = -0.80[/tex][tex]Z = -0.80[/tex] has a pvalue of 0.2119.So, there is a 21.19% probability that X the mean weight is lighter than 149 lb.And a 1-0.2119 = 0.7881 = 78.81% probability that the boat is overloaded because the 70 passengers have a mean weight greater than 149 lb.