2. Plastic drinking straws are manufactured to fit into drinks cartons which have a hole in the top. A straw fits into the hole if the diameter of the straw is less than 3 mm. The diameters of the straws have a normal distribution with mean 2.6 mm and standard deviation 0.25 mm. (a) A straw is chosen at random. Find the probability that it fits into the hole in a drinks carton. (b) 500 straws are chosen at random. Use a suitable approximation to find the probability that at least 480 straws fit into the holes in drinks cartons.

2. Plastic drinking straws are manufactured to fit into drinks cartons which have a hole in the top. A straw fits into the hole if the diameter of the straw is less than 3 mm. The diameters of the straws have a normal distribution with mean 2.6 mm and standard deviation 0.25 mm. (a) A straw is chosen at random. Find the probability that it fits into the hole in a drinks carton. (b) 500 straws are chosen at random. Use a suitable approximation to find the probability that at least 480 straws fit into the holes in drinks cartons.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Sketch the distribution, show the mean and standard error, and shade the part of the curve corresponding to your calculation. Suppose that at a large university, 34% of the students decide to take their classes online. 2. Now, if the researcher takes a different sample of 1000 students, what is the probability that at least 35% of the new sample will decide to take classes online?
The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410? A B I 흐 흐흐 #1 1 I OC US X₂ x²
An instructor gives a test to a class containing several hundred students. It is known that the standard deviation of the scores is 14 points. A random sample of 49 scores is obtained. a. What is the probability that the average score of the students in the sample will differ from the overall average by more than 2 points? b. What is the probability that the average score of the students in the sample will be within 3 points of the overall average?
A rugby team from the country of Atlantis is formed by randomly drawing from its population. The population distribution is normally distributed with a mean of 165 cm and a standard deviation of 10 cm. The team draws 26 people for the team. What is the probability that the sample mean is less than 163? Give your answer to four decimal places.
A particular fruit's weights are normally distributed, with a mean of 360 grams and a standard deviation of 28 grams.If you pick 7 fruit at random, what is the probability that their mean weight will be between 342 grams and 360 grams
An elevator has a placard stating that the maximum capacity is 4400 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4400/29 = 152 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 152 lb is ☐ (Round to four decimal places as needed.)
Malaysian families recorded an average of 17.2 kg of glass garbage each year with the standard deviation of the distribution is 2.5 kg. Using a central limit theorem, compute a probability that the mean of a sample of 55 families will be between 17 kg and 18 kg.
An elevator has a placard stating that the maximum capacity is 3800 lb—26 passengers. So, 26 adult male passengers can have a mean weight of up to 3800/26=146 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 39 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 146 lb. b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 146 lb. c. What do you conclude about the safety of this elevator?
Suppose that you have a large number of potatoes. The mean weight of the potatoes is 7.4 ounces with a standard deviation of 2.2 ounces. We may assume a normal distribution. b) If you choose 45 potatoes at random, what is the probability that the mean of this sample of 45 potatoes is less than 7 ounces?
The weights of all the turkeys sold in Fairfax County in 2020 were recorded in the data set “Fairfax Turkey Weights” found in the histogram. The weights are presented in pounds. There are 235,428 turkeys in this population. Calculate the probability that, in a random sample of eight turkeys, the mean weight is between 17 and 20 pounds. First, draw a picture with the rounded mean and values labeled and the shaded area representing the desired probability. Next, take a picture of your hand drawn sketch and upload it (if you do not have this technology, you may use any other method (i.e. Microsoft paint) to sketch the image). Then, complete this part by standardizing and using the Standard Normal Table to obtain this probability. Show your work “by hand”.
An elevator has a placard stating that the maximum capacity is 4100 lb-27 passengers. So, 27 adult male passengers can have a mean weight of up to 4100/27= 152 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 27 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? Round to four decimal places as needed
III. SAMPLING AND SAMPLING DISTRIBUTIONS Assume that the systolic blood pressure of 30-year-old males is normally distributed, with an average of 122 mmHg and a standard deviation of 10 mmHg. а. b. Calculate the probability that the blood pressure of an individual male from this population will be between 118 and 124 mmHg.