MATH SOLVE

2 months ago

Q:
# (CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20.1 ounces and a standard deviation of 0.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces? 0.553 0.748 0.252 0.447

Accepted Solution

A:

Answer:The probability is 0.252 ⇒ 3rd answerStep-by-step explanation:* Lets revise how to find the z-score- The rule the z-score is z = (M - μ)/σM , where# M is the sample mean# μ is the mean# σM is the standard deviation of the sample mean (standard error)- The rule of σM = σ/√n , where n is the sample size* Lets solve the problem∵ The mean weight is 20.1 ounces∴ μ = 20.1∵ The standard deviation is 0.3 ounces∴ σ = 0.3∵ You randomly select 25 cartons∴ n = 25∵ Their mean weight is greater than 20.06∴ M = 20.06- Lets find σM∵ σM = σ/√n∴ σM = 0.3/√25 = 0.3/5 = 0.06- Lets find z-score ∵ z-score = (M - μ)/σM∴ z-score = (20.06 - 20.1)/0.06 = -0.04/0.06 = - 0.6670- To find P(M > 20.06) you will asking to find the proportion of area under the standard normal distribution curve for all z-scores > -0.670- It can be read from a z-score table by referencing a z-score of -0.670- Look to the attached table∴ P(M > 20.06) = 0.2514* The probability is 0.252