The number of peanuts in bags is normally distributed with a mean of 193.8 peanuts and a standard deviation of 4.1 peanuts. What is the z-score of a bag containing 185 peanuts?

2.47

2.15

1.90

1.22

Question

The number of peanuts in bags is normally distributed with a mean of 193.8 peanuts and a standard deviation of 4.1 peanuts. What is the z-score of a bag containing 185 peanuts?

       2.47

       2.15

       1.90

       1.22

anonymous · Answer

@math&ing001

anonymous · Answer

Heights of certain plants at a nursery are normally distributed with a mean of 52.5 centimeters and a standard deviation of 7.2 centimeters. If their z-scores are greater than 2.25, the plants are displayed in the main lobby. To the nearest centimeter, what is the minimum required height for this type of plant to be displayed in the main lobby?
)
       69 cm

       68 cm

       56 cm

       55 cm

anonymous · Answer

just these two

anonymous · Answer

The first problem is just applying the transformation $Z=\dfrac{X-\mu}{\sigma}$. In this case you have $\mu=198.8$ and $\sigma=4.1$, with $X=185$. Simple algebra.

The second problem uses the same transformation, but this time you solve for $X$. Given $\mu=52.5$ and $\sigma=7.2$, find $X$ when $Z=2.25$.