Question

In: Math

he number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally...

he 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 1100 and 1400 chocolate​ chips, inclusive?

​(b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate​ chips?

​(c) What proportion of bags contains more than 1200 chocolate​ chips?

​(d) What is the percentile rank of a bag that contains 1050 chocolate​ chips?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 1252

standard deviation = = 129

a) P(1100 < x < 1400) = P[(1100 - 1252) / 129) < (x - ) /  < (1400 - 1252) / 129) ]

= P(-1.18 < z < 1.15)

= P(z < 1.15) - P(z < -1.18)

Using z table,

= 0.8749 - 0.119

= 0.7559

b) P(x < 1025) = P[(x - ) / < (1025 - 1252) /129 ]

= P(z < -1.76)

Using z table,

= 0.0392

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

=1- p P[(x - ) / < (1200 - 1252) / 129]

=1- P(z < -0.40)

Using z table,

= 1 - 0.3446

= 0.6554

d) x = 1050

Using z-score formula,

z = x - /   

z = 1050 - 1252 / 129

z = -1.57

= P(z < -1.57)

Using z table,

= 0.0582

The percentage is = 5.82%

percentile rank is = 6th


Related Solutions

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally...
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. d) What is the percentile rank of a bag that contains 1450 chocolate​ chips?
the number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally...
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 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1175 chocolate chips? (d) what is the percentile rank of...
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally...
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 of 129 chips. a. What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips? b. What is the probability that a randomly selected bag contains more than 1225 chocolate chips? c. What is the percentile rank of a bag that contains 1425 chocolate chips Suppose the lengths of...
The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally...
The number of chocolate chips in an​ 18-ounce bag of chocolate 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 1000 and 1400 chocolate​ chips? ​ (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate​ chips? ​ (c) What proportion of bags contains more than 1225 chocolate​ chips? ​(d) What is the percentile rank of a...
the number of chocolate chips in an 18 oz bag of chocolate chip cookies is approximately...
the number of chocolate chips in an 18 oz bag of chocolate chip cookies is approximately normally distributed with 1270 in the standard deviation is 130 chips what is the probability that a randomly-selected bag contains no more than 1200 chips what is the probability that a randomly-selected bag of 30 bags has a random mean that's no more than 1200 chips what number of chocolate chips in a bag will correspond to the 15th percentile
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed...
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1263 and a standard deviation of 118. ​(a) Determine the 29th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 97% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed...
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. ​(a) Determine the 28th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 96​% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed...
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. ​(a) Determine the 29th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 98​% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?
2. The number of chocolate chips in a bag of chocolate chip cookies is approximately normally...
2. The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips Part (a): About how many percent of the cookie bags are in between 1200 and 1300 chips. Part (b): Determine the 30th percentile for the number of chocolate chips in a bag. Part (c): Determine the minimum number of chocolate chips in a bag that make up the middle 95...
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed...
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1263 and a standard deviation of 118. ​(a) Determine the 2929th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 97​% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT