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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 315 grams and a standard deviation of 16 grams. Find the weight that corresponds to each event.

a. Highest 20 percent
b. Middle 60 percent to
c. Highest 80 percent
d. Lowest 15 percent

Respuesta :

okpalawalter8

The solution to the questions are

  • X'= 301.5341
  • X"= 328.4659
  • X'''= 301.5341
  • X''''= 298.4171

What is the Highest 20 percent ?

Generally, the equation for the mean is  mathematically given as

The following is the formula for determining the X score:

X = Mean + Z*SD

Part a

The value of 0.841621 is assigned as the Z-score for the top 20%. (using excel)

X = 315 + 0.841621*16

X= 328.4659

Part b

The Z-scores range from -0.84162 to 0.841621 for the middle 60 percent of the population (using excel)

X '= 315 - 0.841621*16

X'= 301.5341

X" = 315 + 0.841621*16

X"= 328.4659

c)

The value of -0.84162 is assigned as the Z score for the top 80 percent (by using excel)

X''' = 315 - 0.841621*16

X'''= 301.5341

d)

The Z score for the group comprising the worst 15 percent is written as -1.03643. (by using excel)

X'''' = 315 – 1.03643*16

X''''= 298.4171

In conclusion,

  • X'= 301.5341
  • X"= 328.4659
  • X'''= 301.5341
  • X''''= 298.4171

Read more about standard deviation

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