Question

In: Statistics and Probability

Weights of men are normally distributed with a mean of 180 pounds and a standard deviation...

Weights of men are normally distributed with a mean of 180 pounds and a standard deviation of 25 pounds. A boat in Michigan will sink if the average weight of its 20 passengers is over 200 pounds. What is the probability that a group of 20 men will have an average weight greater than 200 pounds?

Expert Solution

Solution :

Given that,

mean = = 180

standard deviation = =25

n=20

= =180

= / n =25 / 20= 5.5902

P( >200 ) = 1 - P( < 200)

= 1 - P[( - ) / < (200 -180) / 5.5902]

= 1 - P(z <3.58 )

Using z table

= 1 - 0.9998

= 0.0002

probability= 0.0002

orchestra answered 2 years ago

Weights of men are normally distributed with a mean of 189 lb and a standard deviation...

Weights of men are normally distributed with a mean of 189 lb and a standard deviation of 39 lb. If 14 men are randomly selected, find the probability that they have weights with a mean greater than 174 lb.

Men’s weights are normally distributed with mean 175 pounds and standard deviation 25 pounds. (a) Find...

Men’s weights are normally distributed with mean 175 pounds and standard deviation 25 pounds. (a) Find the probability that a randomly selected man has a weight between 140 and 190. (Show work and round the answer to 4 decimal places) (b) What is the 80th percentile for men’s weight? (Show work and round the answer to 2 decimal places) (c) If 64 men are randomly selected, find the probability that sample mean weight is greater than 180. (Show work and...

1) The weights of bowling balls are normally distributed with mean 11.5 pounds and standard deviation...

1) The weights of bowling balls are normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. A sample of 36 bowling balls is selected. What is the probability that the average weight of the sample is less than 11.07 pounds? 2) According to one pollster, 46% of children are afraid of the dark. Suppose that a sample of size 20 is drawn. Find the value of standard error , the standard deviation of the distribution of sample proportions.

The weight of Bluefin Tuna is approximately normally distributed with mean 32 pounds and standard deviation...

The weight of Bluefin Tuna is approximately normally distributed with mean 32 pounds and standard deviation 5 pounds. Answer the following questions: 1a. How much does a fish have to weigh to fall into the 75 percentile? (Inverse) a) 32.37 b) 35.37 c) 32.75 d) 38.7 1b. The record catch for a Tuna is 511 pounds. What are the chances of that happening? Find the z score. a) 504.6 b) 95.8 c) 94 d) 100 1c. In the sample of...

The weights of Delicious Chocolate Bars are approximately normally distributed with mean 54g and standard deviation...

The weights of Delicious Chocolate Bars are approximately normally distributed with mean 54g and standard deviation 14g. They are sold in packs of a 12 bars. One pack of 12 is selected at random. Assume this pack can be regarded as a random sample of 12 chocolate bars. Part A What is the expected value for the mean weight of chocolate bars in this pack? Give your answer to the nearest whole number in the form x or xx as...

The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and...

The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 900lbs. Find the probability that the weight of a randomly selected steer is between 1200 and 1530lbs. Round your answer to four decimal places.

The weights for newborn babies is approximately normally distributed with a mean of 6.9 pounds and...

The weights for newborn babies is approximately normally distributed with a mean of 6.9 pounds and a standard deviation of 1.1 pounds. Consider a group of 1200 newborn babies: 1. How many would you expect to weigh between 6 and 9 pounds? 2. How many would you expect to weigh less than 8 pounds? 3. How many would you expect to weigh more than 7 pounds? 4. How many would you expect to weigh between 6.9 and 10 pounds?

The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and...

The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds. Consider a group of 1100 newborn babies: 1. How many would you expect to weigh between 4 and 8 pounds? 2. How many would you expect to weigh less than 7 pounds? 3. How many would you expect to weigh more than 6 pounds? 4. How many would you expect to weigh between 6.4 and 10 pounds?

The heights of men are normally distributed with a mean of 68.6 in and a standard...

The heights of men are normally distributed with a mean of 68.6 in and a standard deviation of 2.8 in. If a man is randomly selected, find the probability that his height is at least 71 in.

Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4...

Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be between 64 inches and 77 inches. Make sure you are rounding z-scores properly to two places. Part A: Find the two z-scores for women who meet this height requirement z = (smaller value) and z = (larger value) Part B:...