Question

In: Math

The number of peanut M&Ms in a 2 ounce package is normally distributed with a mean...

The number of peanut M&Ms in a 2 ounce package is normally distributed with a mean of 28 and standard deviation 2; The number of Skittles in a 2 ounce package is normally distributed with a mean of 60 and standard deviation 4.

Questions 1-3: Suppose that I purchase two 2-ounce packages of peanut M&Ms and one 2-ounce package of Skittles.

1. Let X= the total number of pieces of candy in all three bags combined. What is the distribution of X?

2. What is the probability that the total number of pieces of candy in all three bags combined is less than 110?

3. What is the probability that the total number of M&Ms (in both bags combined) is greater than the number of Skittles?

Solutions

Expert Solution

here,

for 2-ounce packages of peanut M&Ms

A ~ N(28,22) and

for 2-ounce package of Skittles

B ~ N(60,42)

1) Let X= the total number of pieces of candy in all three bags combined

so,

X = 2A + B

E(X) = 2E(A)+E(B) = 2*28+60= 116

V(X) = 4V(A)+V(B) = 4*4+16 =32

standard devaition, s = sqrt(V(X)) = sqrt(32) = 5.66

so,

X ~N(116,32)

----------------------------------------------------------------------------------------------------------------------------------

2) P(X < 110) = P(Z < (110 - 116)/5.66) = P(Z < -1.06) = 0.1446

----------------------------------------------------------------------------------------------------------------------------------

3) P(2A > B) = P(2A - B > 0) = P(U > 0)

here, E(X) = 2A - B = 2E(A) - E(B) = -4

P(2A > B) = P(Z > (0-(-4))/5.66) = P(Z > 0.7067) = 0.2399 (if it is incorrect round the Z value to 2 decimal places and calculate p value)


Related Solutions

The number of M&M's in a package normally distributed with a mean of 48 candies and...
The number of M&M's in a package normally distributed with a mean of 48 candies and a standard deviation of 3. Lets say that we get 40 packages of M&M's. What is the probability that the average number of candies in those 40 packages is between 46 and 49? 0.49999 0.9825 0.3781 0.96499
Q.N. 7) According to the manufacturer of M& Ms, 12% of the peanut M&Ms in a...
Q.N. 7) According to the manufacturer of M& Ms, 12% of the peanut M&Ms in a bag should be brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. A student randomly selected a bag of peanut M&Ms. He counted the number of M&Ms that were each color and obtained the results shown in the table below. Test whether peanut M&Ms follow the distribution stated by M&M/Mars at the α = 0.05 level of significance. Color Frequency Brown...
**Assume that both Plain and Peanut M&M candies are normally distributed. 1. Suppose that M&M claims...
**Assume that both Plain and Peanut M&M candies are normally distributed. 1. Suppose that M&M claims that their Plain M&Ms have an equal proportion of red and brown. a. Test the claim that the proportion of red M&Ms is greater than the proportion of brown M&Ms. b. Test the claim that the proportion of red M&Ms is less than the proportion of brown M&Ms. Total number of M&M's: 665 Total number of red M&M's: 76 Total number of brown M&M's:...
The number of raisins in a 16-ounce bag of oatmeal raisin cookies is normally distributed with...
The number of raisins in a 16-ounce bag of oatmeal raisin cookies is normally distributed with a mean of 1021 raisins and a standard deviation of 2101 raisins. a. What proportion of 16-ounce bags of oatmeal raisin cookies contain fewer than 900 raisins? b. What is the probability that 14 random selected bags of oatmeal raisin cookies contain on average fewer than 900 raisins? c. Which is more likely: choosing a bag with fewer than 900 raisins, or choosing 14...
According to Masterfoods, the company that manufactures M&Ms, 12% of peanut M&Ms are brown, 15% are...
According to Masterfoods, the company that manufactures M&Ms, 12% of peanut M&Ms are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. Assume that selecting multiple M&Ms are independent events. (Round your answers to three decimal places, for example: 0.123) Compute the probability that a randomly selected peanut M&M is not yellow. A: Compute the probability that four randomly selected peanut M&Ms are all yellow. A: If you randomly select five peanut...
The number of ants per acre in the forest is normally distributed with mean 45,000 and...
The number of ants per acre in the forest is normally distributed with mean 45,000 and standard deviation 12,278. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected acre in the forest has fewer than 57,834 ants. c. Find the probability that a randomly selected acre has between...
The number of ants per acre in the forest is normally distributed with mean 43,000 and...
The number of ants per acre in the forest is normally distributed with mean 43,000 and standard deviation 12,405. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected acre in the forest has fewer than 55,888 ants. c. Find the probability that a randomly selected acre has between...
the number or interviews recieved by a college graduating class is normally distributed with a mean...
the number or interviews recieved by a college graduating class is normally distributed with a mean of 8 interviews , standard deviation of 2 interviews 15% of all graduates recieve more than how many interviews?
the weight of a large number of miniature poodles are approximately normally distributed with a mean...
the weight of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 Kg measurments are recorded to the nearest tenth of a kilogram. a)draw a sketch of the distribution of poodle weights b)what is the chance of a poodle weight over 9.8Kg? c)what is the chance a poodle weight between 7.1 and 8.9 kilogram d)75% of poodles weigh more than what weight
The number of letters handled daily by a post office is normally distributed with a mean...
The number of letters handled daily by a post office is normally distributed with a mean of 20,000 letters and a standard deviation of 100 letters. Find the percent of days on which the post office handles: A.) more than 20,200 letters B.) fewer than 19,900 letters C.) Between 19,950 and 20,050 letters D.) between 20,100 and 20,150 letters
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT