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Question 4 (25 marks) A candy factory produces a popular candy. Suppose that the weight of a bag of candy from the production line of the factory follows a normal distribution with mean 371 grams and standard deviation 23 grams. (a) What is the probability that a bag of candy weighs between 365 and 380 grams? (b) As a routine check, a random sample of 55 bags of candy is selected. What is the probability that the sample mean weight is greater than 380 grams? (c) Suppose the selected 55 bags of candy in (b) gave a mean 373.2 grams and a standard deviation 18.63 grams. At 1% level of significance, test whether the mean weight is greater than 371 grams. (d) The production engineer wants to maintain the mean at 371 grams and adjust only the value of standard deviation so that only 4% of the weight of a bag is greater than 400 grams. Find the adjusted standard deviation. 

          Question 4 (25 marks)
A candy factory produces a popular candy. Suppose that the weight of a bag of candy from the production line of the factory follows a normal distribution with mean 371 grams and standard deviation 23 grams.

(a) What is the probability that a bag of candy weighs between 365 and 380 grams?

(b) As a routine check, a random sample of 55 bags of candy is selected. What is the probability that the sample mean weight is greater than 380 grams?

(c) Suppose the selected 55 bags of candy in (b) gave a mean 373.2 grams and a standard deviation 18.63 grams. At 1% level of significance, test whether the mean weight is greater than 371 grams.

(d) The production engineer wants to maintain the mean at 371 grams and adjust only the value of standard deviation so that only 4% of the weight of a bag is greater than 400 grams. Find the adjusted standard deviation.
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Question 4 (25 marks) A candy factory produces a popular candy. Suppose that the weight of a bag of candy from the production line of the factory follows a normal distribution with mean 371 grams and standard deviation 23 grams. (a) What is the probability that a bag of candy weighs between 365 and 380 grams? (b) As a routine check, a random sample of 55 bags of candy is selected. What is the probability that the sample mean weight is greater than 380 grams? (c) Suppose the selected 55 bags of candy in (b) gave a mean 373.2 grams and a standard deviation 18.63 grams. At 1% level of significance, test whether the mean weight is greater than 371 grams. (d) The production engineer wants to maintain the mean at 371 grams and adjust only the value of standard deviation so that only 4% of the weight of a bag is greater than 400 grams. Find the adjusted standard deviation.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Question 4 (25 marks) A candy factory produces a popular candy. Suppose that the weight of a bag of candy from the production line of the factory follows a normal distribution with mean 371 grams and standard deviation 23 grams. (a) What is the probability that a bag of candy weighs between 365 and 380 grams? (b) As a routine check, a random sample of 55 bags of candy is selected. What is the probability that the sample mean weight is greater than 380 grams? (c) Suppose the selected 55 bags of candy in (b) gave a mean 373.2 grams and a standard deviation 18.63 grams. At 1% level of significance, test whether the mean weight is greater than 371 grams. (d) The production engineer wants to maintain the mean at 371 grams and adjust only the value of standard deviation so that only 4% of the weight of a bag is greater than 400 grams. Find the adjusted standard deviation.
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Transcript

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00:01 Hello students, today we will discuss about this question.
00:04 In this question we are given that a chocolate factory produces a popular chocolate.
00:10 Suppose the weight of a bag of candy from the production line of the factory follows a normal distribution with a mean is equal to 3 .7 .1 gram and the standard deviation, that is standard deviation, is equal to 23 grams.
00:32 First of all we need to find the probability that the bag of chocolate weight between 365 and 380 gram that is equal to question mark so therefore we can write probability of 365 less than axis less than 380 is equal to question mark and here in part b as a routine check a random sample of n that is equals to 55 bags of chocolate is selected then we need to find the probability that the sample mean weight is greater than 380 so therefore we can write the probability of z x bar probability of x bar is greater than 380 is equal to question mark so here first of all for the part a we can say that let x be the weight of the bag of the candy from the production line of the factory that follows a normal distribution with mu is equals to 371 and sigma that is equals to 23.
01:51 The probability that the bag of the chocolate weights between 365 to 380 so that for probability of 365 less than x less than 380 is equal to probability of 365 minus 371 divided by 23 less than x.
02:10 X minus mu divided by sigma less than 380 minus 371 divided by 23 so that is equals to probability of minus 0 .2609 less than z less than 0 .3913 so that is equals to we can write probability of z is less than or equals to 0 .3913 minus probability of z is less than or equals to 0 .31913 minus probability of z is less than or equals to 0 .2609 so that is equals to we will get 0.
02:42 So this will be our required answer for the part a...
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