Question

In: Statistics and Probability

The weights of scones in another Box are normally distributed with mu and standard deviation 0.4...

The weights of scones in another Box are normally distributed with mu and standard deviation 0.4 g. It is known that 10% of the scones in this Box weigh less than 4 g. Find the value of mu

Solutions

Expert Solution

Let X denote the weight of scone in box. Given X has normal distribution with mean and standard deviation .

Then has standard normal distribution.

Given

Then

where Z is standard normal random variable.

From standard normal table

Comparing this we get


Related Solutions

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.
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.
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?
The weights of steers in a herd are distributed normally. The standard deviation is 300 lbs...
The weights of steers in a herd are distributed normally. The standard deviation is 300 lbs and the mean steer weight is 1100 lbs. Find the probability that the weight of a randomly selected steer is greater than 1456 lbs. Round your answer to four decimal places.
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 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...
A process is known to produce bricks whose weights are normally distributed with standard deviation 0.12...
A process is known to produce bricks whose weights are normally distributed with standard deviation 0.12 pounds. A random sample of sixteen bricks from today's output had a mean weight of 4.07 pounds. Find a 99% confidence interval for the mean weight of all bricks produced today. (6) Without doing the calculations, state whether a 95% confidence interval for the population mean would be wider than, narrower than, or the same width as that found in (a). (2) It is...
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...
Assume the random variable X is normally​ distributed, with mean mu=49 and standard deviation sigma=7. Find...
Assume the random variable X is normally​ distributed, with mean mu=49 and standard deviation sigma=7. Find the 10 th percentile.
a. A population is normally distributed with a mean of 16.4 and a standard deviation of...
a. A population is normally distributed with a mean of 16.4 and a standard deviation of 1.4. A sample of size 36 is taken from the population. What is the the standard deviation of the sampling distribution? Round to the nearest thousandth. b. A population is normally distributed with a mean of 15.7 and a standard deviation of 1.4. A sample of size 24 is taken from the population. What is the the standard deviation of the sampling distribution? Round...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT