Respuesta :
Answer:
Explained below.
Step-by-step explanation:
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and standard deviation 118 chips.
(a)
Compute the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips as follows:
[tex]P(1000<X<1400)=P(\frac{1000-1262}{118}<\frac{X-\mu}{\sigma}<\frac{1400-1262}{118})\\\\=P(-2.22<Z<1.17)\\\\=P(Z<1.17)-P(Z<-2.22)\\\\=0.87900-0.01321\\\\=0.86579\\\\\approx 0.8658[/tex]
Thus, the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips is 0.8658.
(b)
Compute the probability that a randomly selected bag contains fewer than 1000 chocolate chip as follows:
[tex]P(X<1000)=P(\frac{X-\mu}{\sigma}<\frac{1000-1262}{118})\\\\=P(Z<-2.22)\\\\=0.01321\\\\\approx 0.0132[/tex]
Thus, the probability that a randomly selected bag contains fewer than 1000 chocolate chip is 0.0132.
(c)
Compute the proportion of bags that contains more than 1200 chocolate chips as follows:
[tex]P(X>1200)=P(\frac{X-\mu}{\sigma}>\frac{1200-1262}{118})\\\\=P(Z<-0.53)\\\\=0.29806\\\\\approx 0.2981[/tex]
Thus, the proportion of bags that contains more than 1200 chocolate chips is 0.2981.
(d)
Compute the percentile rank of a bag that contains 1125 chocolate chips as follows:
[tex]P(X<1125)=P(\frac{X-\mu}{\sigma}<\frac{1125-1262}{118})\\\\=P(Z<-1.16)\\\\=0.12302\\\\\approx 0.123[/tex]
Thus, the percentile rank of a bag that contains 1125 chocolate chips is 12.3rd.
