**Normal Distribution of Mouse Mass**The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.3 grams and a standard deviation of 0.1 grams.### Probability CalculationsFor parts (a) through (c), enter your responses as a decimal with 4 decimal places.**a)** What is the probability that a randomly chosen mouse has a mass of less than 20.23 grams?```[INPUT BOX]```**b)** What is the probability that a randomly chosen mouse has a mass of more than 20.42 grams?```[INPUT BOX]```**c)** What proportion of mice have a mass between 20.22 and 20.37 grams?```[INPUT BOX]```

The mean is 20.3 and the standard deviation is 0.1.

Answered: The mass of a species of mouse commonly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 4 inches. A random sample of 26 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean?
The length of a fully grown nibiscus plants is normally distributed and has a mean of 35cm. It is found that 5% of these plants are longer than 45cm. i. When plants are chosen for sale, those shorter than 30cm are rejected. Find the probability that a plant will be rejected. Find the standard deviation o. ii.
Assume that the height of a type of tree has a normal probability distribution with a mean of 85.9 ft and a standard deviation of 9.4 ft. A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 3 decimal places.
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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
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2.4 and a mean diameter of 209 inches. If 69 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.1 inches? Round your answer to four decimal places. use ti 84 device
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.)
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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
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