$\mathbb P(X>600)=\mathbb P\left(\dfrac{X-510}{85}>\dfrac{600-510}{85}\right)=\mathbb P(Z>1.059)\approx0.145$

So approximately 14.5% of the scores are higher than 600. This means in a sample of 7500, one could expect to see $0.145\times7500\approx10.86$ scores above 600.

5 0

3 years ago

Identify the domain and range to the following relations and state whether or not the relations are functions. State why or why

Vladimir79 [104]

It’s a function because it passes the vertical line test

6 0

2 years ago

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pound

DanielleElmas [232]

Answer:

There are 118 plants that weight between 13 and 16 pounds

Step-by-step explanation:

For any normal random variable X with mean μ and standard deviation σ : X ~ Normal(μ, σ)

This can be translated into standard normal units by :

$Z = \frac{(X - \mu)}{\sigma}$

Let X be the weight of the plant

X ~ Normal( 15 , 1.75 )

To find : P( 13 < X < 16 )

$= P(\frac{( 13 - 15 )}{1.75} < Z < \frac{( 16 - 15 )}{1.75})$

= P( -1.142857 < Z < 0.5714286 )

= P( Z < 0.5714286 ) - P( Z < -1.142857 )

= 0.7161454 - 0.1265490

= 0.5895965

So, the probability that any one of the plants weights between 13 and 16 pounds is 0.5895965

Hence, The expected number of plants out of 200 that will weight between 13 and 16 = 0.5895965 × 200

= 117.9193

Therefore, There are 118 plants that weight between 13 and 16 pounds.

4 0

3 years ago