We know that if
, then
Let X denote the weight of a package (in pounds).
Now,
So,
Using Central Limit theorem, we know,
Required probability =
We load on a plane 100 packages whose weights are independent random variables between 20 and...
The weights of packages shipped via a national delivery company follows a normal distribution with mean 24.6 pounds and standard deviation 4 pounds. a.) What is the probability that a randomly selected package will weigh more than 25 pounds? b.) A local delivery truck has a capacity of 7,250 pounds. If 290 packages are loaded onto the truck, what is the probability that the weight capacity will be exceeded?
A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.03 of falling outside the specification and that the weights of the packages are independent. a. What is the probability that the process continues to run until the 120th package is being processed? b. Find the mean number of packages that will be filled before the process is stopped.
1) The weights of newborn children in the U.S. vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies newborns as having low birth weight if the weight is less than 5.5 pounds. a) What is the probability that a baby chosen at random weighs less than 5.5 pounds at birth? b) Suppose we select 10 babies at random. What is the probability that their average birth weight is less than 5.5...
162-60-102 6. Total: 6 points. The weights of packages carried by UPS courier service has a normal distribution with a mean of 17.2 ounces and a standard deviation of 6.3 ounces. (3 peo) It is proposed that packages weighing over 24 ounces will be subjected to a surcharge. What proportion of packages will be affected by the surcharge? u=17.2 o=6.3 a P(x>24) = P(Z >24-17, 2) = P(Z >1.08) =.140 b. (3 pts) A random sample of 20 packages is...
Say we have data xi, . . ,z,, which are independent and identically distributed normal random variables with mean μ and variance 100. How often does this interval cover 11, 20
Say we have data xi, . . ,z,, which are independent and identically distributed normal random variables with mean μ and variance 100. How often does this interval cover 11, 20
1. Let X be a normal random variable with mean 16. If P(X < 20) 0.65, find the standard deviation o. 2. The probability that an electronic component will fail in performance is 0.2 Use the normal approximation to Binomial to find the probability that among 100 such components, (a) at least 23 will fail in performance. X 26) (b) between 18 and 26 (inclusive) will fail in performance. That is find P(18 3. If two random variables X and...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Question 1 5 pts The weights of creatures on "Planet Zaxorn 245" are very strange. The mean weight of creatures is =3,916 pounds with a standard deviation of o = 696 pounds The weights of these creatures are normally distributed. Determine the weight (i.e. the x-value) a Zaxornian must be lighter than to be in the bottom 2% of weights. Round your answer to two decimal places. Note on "Backward Normal Table" problems: When finding a zed-value associated to a...
a random sample of 25 people whose population average weight is 160 pounds with a standard deviation of 20 pounds would have a standard deviation of the sample mean equal to ? What is the mean of the sampling distribution referred to in question 4?
Patients coming to a medical clinic have a mean weight of 207.6 pounds, with a standard deviation of 22.6 pounds. The distribution of weights is not assumed to be symmetric. Between what two weights does Chebyshev's Theorem guarantees that we will find at least 95% of the patients? Round your answers to the nearest tenth.