Suppose in the milk store, milk sales per day are represented by a random variable X...

Question

Question

Suppose in the milk store, milk sales per day are represented by a random variable X which follows a normal distribution with.

What is the probability that milk sold per day will be between (a) 185 and 245 gallons? And (b) more than 265 gallons?

Mean: 225 gallons

SD: 35 gallons

Please provide a clear explanation with answers.

math Statistics-And-Probability

Answer 1

Answer #1

a) P(185 < X < 245)

= P(-1.14 < Z < 0.57)

= P(Z < 0.57) - P(Z < -1.14)

= 0.7157 - 0.1271

= 0.5886

b) P(X > 265)

= P(Z > 1.14)

= 1 - P(Z < 1.14)

= 1 - 0.8729

= 0.1271

Answer 2

Similar Homework Help Questions

Suppose that the number of gallons of milk sold per day at a local supermarket are...

Suppose that the number of gallons of milk sold per day at a local supermarket are normally distributed with mean and standard deviation of 340.8 and 20.97, respectively. What is the probability that on a given day the supermarket will sell below 334 gallons of milk? Question 1 options: 1) 0.3729 2) 0.6271 3) 0.8208 4) 0.1792 5) We do not have enough information to calculate the value.
9] Suppose X is Normal random variable with mean 10 and SD 4. What is the...

9] Suppose X is Normal random variable with mean 10 and SD 4. What is the probability that X is between 7 and 13? [10] Suppose X is Normal random variable with unknown mean mu and SD 4. For what value of mu, 80th percentile of X will be 23? (11] Lifetime of Carbon 14, X, is modeled by Exponential distribution with mean of 8223.7 years Determine its half-life (50th percentile).
Suppose the number of customers that visit a store in an hour can be represented by...

Suppose the number of customers that visit a store in an hour can be represented by a Poisson random variable with mean 4. What is the probability that the store has no customers for a two-hour period?

Question 1 (0.5 points) A random variable X follows a normal distribution with mean of 50...

Question 1 (0.5 points) A random variable X follows a normal distribution with mean of 50 and standard deviation of 5. Suppose we take a simple random sample of size 6 from the population above. Can we calculate the probability that the sample mean is between 45 and 60? (You do not need to actually calculate the probability for this question.) Yes, and the calculated probability would be exact. Yes, and the calculated probability would be approximate. No. Question 2...
The number of customers entering a store on a given day is Poisson distributed with mean...

The number of customers entering a store on a given day is Poisson distributed with mean 150 . The amount spent in the store by a customer is exponential with mean 200. The amount spent is independent from number of customers . Estimate the probability that the store takes in at least $20,000. Leave the answer in terms of the distribution of he standard normal random variable.
Suppose the number of items you can deliver in a day is a random variable with...

Suppose the number of items you can deliver in a day is a random variable with some unknown distribution with a mean = 35 and a standard deviation of 8. 4.75% of all sample means of 36 days will be less than ?. Group of answer choices 32.7733 37.2267 35.6033 34.3967 36.27 none of these 33.73

Suppose the variable x is represented by a standard normal distribution. What value of x is...

Suppose the variable x is represented by a standard normal distribution. What value of x is at the 60th percentile of the distribution? Equivalently, what is the value for which there is a probability of 0.60 that x will be less than that value? Please round your answer to the nearest hundredth.
1. Suppose the variable x is represented by a standard normal distribution. What is the probability...

1. Suppose the variable x is represented by a standard normal distribution. What is the probability of x < -0.6? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12). 2. The mean is 55.3 and the standard deviation is 9.2 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 65?
Suppose that a random variable X follows a distribution with mean 100 and variance 81. We...

Suppose that a random variable X follows a distribution with mean 100 and variance 81. We take a random sample of 240 observations and calculate x. What is the probability that we calculate a sample mean larger than 101?

(5.) You run a store that sells Christmas trees for Sd each. Suppose the number of...

(5.) You run a store that sells Christmas trees for Sd each. Suppose the number of customers that enter your store on a given day is described by a Poisson random variable with parameter λ. Further, suppose that each customer buys a tree with probability p, and that all customers are independent. (a) What is the expected number of customers that enter your store on a given day? (b) What is your expected revenue for a single day (revenue is...