Question

Men have an average weight of $172$pounds with a standard deviation of $29$pounds.

a. Find the probability that $20$randomly selected men will have a sum weight greater than $3600$lbs.

b. If $20$ men have a sum weight greater than $3500$lbs, then their total weight exceeds the safety limits for water taxis. Based on (a), is this a safety concern? Explain.

Short answer

(a)$1-.8913=0.1087$

(b) If the$20$men's sum weight greater than $3500\mathrm{lbs}$exceeds then it will exceeds the safety limits for water taxis because the probability will be less. Hence it is a safety concern.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, Men have an average weight of $172$ pounds with a standard deviation of $29$ pounds.

Part (a) Step 2: Explanation

According to the provided details, average weight is $\mu =172$pounds, standard deviation $\sigma =29$pounds.

Use the T I-83 calculator to determine the likelihood that 20 randomly picked males will have a total weight more than$3600\mathrm{lbs}$, To do so, go to $2^{\text{nd}}$,then DISTR, and then scroll down to the normalcdf option and fill in the required information. After that, press the calculator's ENTER key to get the desired result. The following is a screenshot:

Therefore, the probability that $20$randomly selected men will have a sum weight greater than $3600$labs is approximately:$1-.8913=0.1087\text{.}$

Part (b) Step 1: Given information 

Given in the question that, Men have an average weight of $172$ pounds with a standard deviation of $29$ pounds.

Part (b) Step 2: Explanation

According to the provided details, average weight is $\mu =172$pounds, standard deviation $\sigma =29$pounds.

The chance that the localid="1650523973808" $20$males chosen at random will have a total weight of more than localid="1650523978429" $3600$labs is about localid="1650523981580" $1\%$. As a result, if the total weight of the localid="1650523985133" $20$guys surpasses localid="1650523988819" $3500lbs$, it will exceed the safety restrictions for water taxis because the chance will be lower. As a result, it's a safety issue.