Question

The weights of bags of grasecks chocolate candies are normally distributed with a mean of 4.3 ounces and a standard deviation of 0.05 ounces what is the probability that a bag of these chocolate candies weighs less than 4.27 ounces

Answer 1

Answer: 0.2743

Step-by-step explanation:

Let X be a random variable that represents the weight of bags of grasecks chocolate candoes.

X that follows normal distribution with, Mean = 4.3 ounces, Standard devaition = 0.05 ounces

The probability that a bag of these chocolate candies weighs less than 4.27 ounces :$P(X<4.27) =P(\dfrac{x-\mu}{\sigma}<\dfrac{4.27-4.3}{0.05})$

$=P(z<-0.6)\ \ \ z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(Z<0.6)\\\\=1-0.7257\ [\text{ By p-value table}]\\\\=0.2743$

Hence, the required probability = 0.2743

Answer 2

The probability that a bag of these chocolate candies weighs less than 4.27 ounces is 0.2743

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Let X be a random variable that represents the weight of bags of grasses chocolate candies.

X that follows normal distribution with, Mean = 4.3 ounces, Standard devaition = 0.05 ounces

The probability that a bag of these chocolate candies weighs less than 4.27 ounces :

$P(x < 4.27)=P[\dfrac{x-\mu}{\sigma} < \dfrac{4.27-4.3}{0.05}$

P ( x < 4.27 )   =   P (  z < -0.6  )

P (  x < 4.27  )  =  1  -  P (  z < -0.6 )

P ( x < 4.27 )   =   1  -  0.7257

P ( x < 4.27 )   =  0.2743

Hence,the probability that a bag of these chocolate candies weighs less than 4.27 ounces is 0.2743

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