Question

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1475 chocolate chips? (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive, is nothing. (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1100 chocolate chips is nothing. (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1200 chocolate chips is nothing. (Round to four decimal places as needed.) (d) A bag that contains 1475 chocolate chips is in the nothingth percentile. (Round to the nearest integer as needed.)

Answer #1

**Answer:**

Mean M = 1252

Standard deviation s = 129

Part a)

P(1000 ≤ x ≤ 1400) = P( x≤ 1400) - P( x≤ 1000)

P(x ≤1400) = P(z ≤ (1400-1252)/129)

P(x ≤ 1400) = P(z ≤ 1.15) = 0.8749

P(x ≤ 1000) = P( z ≤ (1000-1252)/129)

P(x ≤ 1000) = P(z ≤ -1.95) = 0.0256

P(1000 ≤ x ≤ 1400) = 0.8749 -0.0256 = 0.8493

Part b)

P(x < 1100) = P(z < (1100-1252)/129)

P(x < 1000) = P(z < -1.18) = 0.1190

Part c)

P( x> 1200) = 1 - P(x < 1200)

P(x < 1175) = P(z < (1200-1252)/129)

P(x < 1175) = P(z < -0.40) = 0.3446

P(x > 1175) = 1 - 0.3446

P( x > 1175) = 0.6554

Part d)

We know that P(X < 1475) = 0.9581 = 0.96

The percentile rank is: 0.96*100

Percentile rank = 96%

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chip cookies is approximately normally distributed with mean 1252
and standard deviation 129 chips.
(a) What is the probability that a randomly selected bag
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contains fewer than 1100 chocolate chips?
(c) What proportion of bags contains more than 1200 chocolate
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chip cookies is approximately normally distributed with a mean of
1252 chips and standard deviation
129 chips.
(a) What is the probability that a randomly selected bag
contains between 1100 and 1500 chocolate chips, inclusive?
(b) What is the probability that a randomly selected bag
contains fewer than 1050 chocolate chips?
(c) What proportion of bags contains more than 1200 chocolate
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chip cookies is approximately normally distributed with mean 1252
and standard deviation 129 chips.
?(a) What is the probability that a randomly
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selected bag contains fewer than 1025 chocolate? chips?
?(c) What proportion of bags contains more than
1200 chocolate? chips?
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contains...

The number of chocolate chips in an 18-ounce bag of chocolate
chip cookies is approximately normally distributed with a mean of
1252 chips and standard deviation 129 chips. (a) What is the
probability that a randomly selected bag contains between 1000 and
1400 chocolate chips, inclusive (b) What is the probability that
a randomly selected bag contains fewer than 1125 chocolate chips
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chip cookies is approximately normally distributed with mean
1252
and standard deviation
129
chips.
(a) What is the probability that a randomly selected bag
contains between
1100
and
1500
chocolate chips?
(b) What is the probability that a randomly selected bag
contains fewer than
1050
chocolate chips?
(c) What proportion of bags contains more than
1200
chocolate chips?
(d) What is the percentile rank of a bag that contains...

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