Question

In: Math

A bridge across a deep jorge has a capacity of 5184 pound. If the weights of...

A bridge across a deep jorge has a capacity of 5184 pound. If the weights of tourists have a mean of 160 pounds and a standard deviation of 38 pounds, find the probability that a group of 32 not-overly-bright tourists who attempts to cross the gorge simultaneously will plummet to a grisly death. (Hint: the groups weight will exceed 5184 pounds if the mean weight in the group is over 162 pounds)

Expert Solution

Solution :

Given that ,

mean = = 160

standard deviation = = 38

n = 32

= = 160

= / n = 38 / 32 = 6.72

P( > 162 ) = 1 - P( < 162 )

= 1 - P[( - ) / < (162 -160) / 6.72]

= 1 - P(z < 0.30 )

Using z table,

= 1 - 0.6179

= 0.3821

milcah answered 10 months ago

A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound...

A company sells ”sports sets” that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pound. The weights average the specified amounts, but the standard deviations are 0.2 pound for the 20-pounders and 0.1 pound for the 5-pounders. We can assume that all the weights are normally distributed. a. The company ships each set to customers in two different containers: The bar is shipped...

The weights of a random sample of cereal boxes that are supposed to weigh 1 pound...

The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are given below. Estimate the standard deviation of the entire population with 91.5% confidence. Assume the population is normally distributed. 1.03, 0.99, 1.03, 1.03, 1.04, 1.03, 0.95, 1.01 LCL = UCL =

A hollow aluminum cylinder 19.0 cm deep has an internal capacity of 2.000 L at 22.0°C....

A hollow aluminum cylinder 19.0 cm deep has an internal capacity of 2.000 L at 22.0°C. It is completely filled with turpentine at 22.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0°C. (The average linear expansion coefficient for aluminum is 24 ✕ 10−6°C−1, and the average volume expansion coefficient for turpentine is 9.0 ✕ 10−4°C−1.) (a) How much turpentine overflows? cm3 (b) What is the volume of turpentine remaining in the cylinder at 80.0°C? (Give...

A hollow aluminum cylinder 24.5 cm deep has an internal capacity of 2.000 L at 17.0°C....

A hollow aluminum cylinder 24.5 cm deep has an internal capacity of 2.000 L at 17.0°C. It is completely filled with turpentine at 17.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 69.0°C. (The average linear expansion coefficient for aluminum is 24 ✕ 10−6°C−1, and the average volume expansion coefficient for turpentine is 9.0 ✕ 10−4°C−1.) (a) How much turpentine overflows? _______cm^3 (b) What is the volume of turpentine remaining in the cylinder at 69.0°C? (Give...

A hollow aluminum cylinder 15.5 cm deep has an internal capacity of 2.000 L at 22.0°C....

A hollow aluminum cylinder 15.5 cm deep has an internal capacity of 2.000 L at 22.0°C. It is completely filled with turpentine at 22.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0°C. (The average linear expansion coefficient for aluminum is 24 ✕ 10−6°C−1, and the average volume expansion coefficient for turpentine is 9.0 ✕ 10−4°C−1.) a) How much turpentine overflows? b) What is the volume of turpentine remaining in the cylinder at 80.0°C? (Give your...

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights...

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 1.6 lb. and 4 oz., or 839 grams. Assume the standard deviation of the weights is 20 grams and a sample of 34 loaves is to be randomly selected. (a) This sample of 34 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution. skewed right approximately...

10. A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the...

10. A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. a. Find the probability that the mean actual weight for the 100 weights is greater than 24.8. (Round your answer to four decimal places. b. Find the 95th percentile for the mean weight for the 100 weights. (Round your answer to...

Consider the knapsack problem with the capacity C = 8 and 5 items with weights 6,...

Consider the knapsack problem with the capacity C = 8 and 5 items with weights 6, 4, 3, 7, 1. Find which items will exactly fill the knapsack using dynamic programming solution introduced in class. Show all your work. use I/O knapsack

The City of San Francisco has two bridges, Golden Gate Bridge and Bay Bridge. Assume these...

The City of San Francisco has two bridges, Golden Gate Bridge and Bay Bridge. Assume these two bridges are designed to survive during earthquakes with magnitude of less than 7 Richter with the probabilities of 0.95 and 0.98. What is the probability that at least one of these two bridges collapse facing an earthquake with magnitude of over 7 Richter?

Jorge Jones, a recent management graduate has a new job as a shelf stocker at the...

Jorge Jones, a recent management graduate has a new job as a shelf stocker at the local Shop and Stop (bad job market). In order to maintain some of the knowledge he gained in college, Jorge wants to apply regression analysis to predict weekly sales on the cereal aisle. He believes there would be a relationship between the shelf space that a particular product takes up and the sales of that product. Jorge has gathered the following data: Shelf Space...