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16 A company produces packets of soap powder which are labeled "Giant Size 32 02. The actual weight of soap powder in a packet iS a normal random variable with...

Question

16 A company produces packets of soap powder which are labeled "Giant Size 32 02. The actual weight of soap powder in a packet iS a normal random variable with a mean of 33 0z. and a standard deviation of 0.7 07 If 97 5% Of packets actually contain more than x ounces Of soap powder; then the value of x is A. 31.628 B. 31.842 C.34372 D. 32.00 E. None of the above

16 A company produces packets of soap powder which are labeled "Giant Size 32 02. The actual weight of soap powder in a packet iS a normal random variable with a mean of 33 0z. and a standard deviation of 0.7 07 If 97 5% Of packets actually contain more than x ounces Of soap powder; then the value of x is A. 31.628 B. 31.842 C.34372 D. 32.00 E. None of the above



Answers

Cereal A company's single-serving cereal boxes advertise 9.63 ounces of cereal. In fact, the amount
of cereal $X$ in a randomly selected box follows a Normal distribution with a mean of 9.70 ounces and
a standard deviation of 0.03 ounces.

(a) Let $Y=$ the excess amount of cereal beyond what's advertised in a randomly selected box, measured in grams $(1 \text { ounce }=28.35 \text { grams). Find the }$ mean and standard deviation of $Y .$
(b) Find the probability of getting at least 3 grams more cereal than advertised.

46. Um um A We know that the meaning of act is a call to 9.7 and some division waxes open toe three. We know that one ounce is equal to 28.35 grams. So the did, um, new variable is aware that conversion between there is equal to 28.35 perhaps Roy, it's excess amount of Syrian Ingrams, and thus we need to decrease that by 9.63 ounce off Syrian. So why would be equal to 28.35 x minus 28.35 watt turbine by 9.63? So this is the relation between Y and and X. If we need to, um can create the meaning. Why so is equal to the mean off 28.35 x minus 20 at minus 273 which is corresponding to 28.35 months of lying by the mean of X urges and my 0.7 a minus at the same 3.145 eso the final answer or the mean value who I will be one point and 9845 center division of wine is equal to 28. Once we find out the blind by the sun that the feeling of acts which is opened or or three this is, um, the answer for, um eight for B question for being question, we need to calculate the probability that that is bigger than we're equal three, which is corresponding to ah, the probability one minus the probability off that is smaller than that. It's smaller than three. As we know the tables for the normal distribution gives the curves for the probability that, yeah, the X or event is smaller than or equal now, bigger than so we right? Ah, that bigger than or equal three in another form one minus B that smaller than three and this, then you can we can get it from the tables. Also, we know that the tables is using instant standardized value. So we have toe, I calculate the small, which is the valiant ST minus the mean James 1.9 it for fine over the standard deviation. Um, which is Ah, opening 850 right. So it is this morning is 1.19 By using the eagles ah, force. It is equal to 1.19 We get that. The probability is ah all point 117 So here we know that this probability one minus four point when 17 so refined that answer would be, Ah, spirit story This from the table. We get this open 883 as you. So here is a reach for the phone. Answer would be open. One one wants it.

Uh huh. The variable is normally distributed with me and mu equals 12 and standard deviation sigma equals 120.5. Based on this information, we want to answer A through C. Below this question is challenge your understanding of the adorable variables are random variables that are normally distributed to solve. We use the information presented on the left and right on the left of information on how to map a Z score onto probability or vice versa. For CNN almost traditions on the right of information relative related to how to map a random variable X. Such as the one we have above, which is not standard normal onto the standard normal Z. You do the conversion given we're utilizing falling left and right to solve So for a what is probably exaggerated than 13 we map onto the Z score excellent over sigma. 30 minutes 12.5 equals two. That's the equivalent question is equivalent to the probabilities is greater than two which is 20.2 to 8 and be what must it be for 99.9% of X to be less than 13. So the probably the lessons, you know, equals 130.999 gives us the score of 3.1. Thus to find a quick sigma we rearrange its expression for the correct value. The stigma is x minus mu over zero equals 13. 12/3 130.1 equals 0.32. To finally and see if sigma stays the same. What must you be? This that 99.9% of x is less than 13 that we're doing the same thing as in part B, but now we're given rearranging from you some U is x minus two. Sigma equals 13 minus 3.1 times 0.5 equals 11.45.

Uh huh. The variable is normally distributed with me and mu equals 12 and standard deviation sigma equals 120.5. Based on this information, we want to answer A through C. Below this question is challenge your understanding of the adorable variables are random variables that are normally distributed to solve. We use the information presented on the left and right on the left of information on how to map a Z score onto probability or vice versa. For CNN almost traditions on the right of information relative related to how to map a random variable X. Such as the one we have above, which is not standard normal onto the standard normal Z. You do the conversion given we're utilizing falling left and right to solve So for a what is probably exaggerated than 13 we map onto the Z score excellent over sigma. 30 minutes 12.5 equals two. That's the equivalent question is equivalent to the probabilities is greater than two which is 20.2 to 8 and be what must it be for 99.9% of X to be less than 13. So the probably the lessons, you know, equals 130.999 gives us the score of 3.1. Thus to find a quick sigma we rearrange its expression for the correct value. The stigma is x minus mu over zero equals 13. 12/3 130.1 equals 0.32. To finally and see if sigma stays the same. What must you be? This that 99.9% of x is less than 13 that we're doing the same thing as in part B, but now we're given rearranging from you some U is x minus two. Sigma equals 13 minus 3.1 times 0.5 equals 11.45.


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