Mathematics, 12.03.2020 00:03, morrowdrew

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 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 1425 chocolate chips?

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answered: makaylahunt

(a) P(1000 < X < 1500) = 0.0256

(b) P(X < 1025) = 0.0392

(d) Percentile rank of a bag that contains 1425 chocolate chips = 90.98%

Step-by-step explanation:

We are given that 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.

Firstly, Let X = number of chocolate chips in a bag

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 1252 chips

$\sigma$ = standard deviation = 129 chips

(a) Probability that a randomly selected bag contains between 1000 and 1500 chocolate chips, inclusive is given by = P(1000 $\leq$ X $\leq$ 1500) = P(X $\leq$ 1500) - P(X < 1000)

P(X $\leq$ 1500) = P( $\frac{ X - \mu}{\sigma}$ $\leq$ $\frac{1500-1252}{129}$ ) = P(Z $\leq$ 1.92) = 0.9726

P(X < 1000) = P( $\frac{ X - \mu}{\sigma}$ < $\frac{1000-1252}{129}$ ) = P(Z < -1.95) = 1 - P(Z $\leq$ 1.95)

= 1 - 0.9744 = 0.0256

Therefore, P(1000 $\leq$ X $\leq$ 1500) = 0.9726 - 0.0256 = 0.947

(b) Probability that a randomly selected bag contains fewer than 1025 chocolate chips is given by = P(X < 1025)

P(X < 1025) = P( $\frac{ X - \mu}{\sigma}$ < $\frac{1025-1252}{129}$ ) = P(Z < -1.76) = 1 - P(Z $\leq$ 1.76)

= 1 - 0.9608 = 0.0392

P(X > 1025) = P( $\frac{ X - \mu}{\sigma}$ > $\frac{1200-1252}{129}$ ) = P(Z > -0.40) = P(Z < 0.40) = 0.6554

(d) Percentile rank of a bag that contains 1425 chocolate chips is given by;

Firstly we will calculate the z score of 1425 chocolate chips, i.e.;

Z = $\frac{1425-1252}{129}$ = 1.34

Now, we will check the area probability in z table which corresponds to this critical value of x;

The value which we get is 0.9098.

Therefore, 90.98% is the rank of bag that contains 1425 chocolate chips.

answered: Guest

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

answered: Guest

sine

step-by-step explanation: