Question

Need help. Not understanding how to start with each of these

Answer 1

Given

mean = 84 pounds

standar deviation = 13 pounds

Procedure

a. New hippo weighs between 90 and 109 pounds

Areas under portions of a normal distribution can be computed by using calculus. Since this is a non-mathematical treatment of statistics, we will rely on computer programs and tables to determine these areas.

`\begin{gathered} \mu=84 \\ \sigma=13 \\ \end{gathered}`

Between 90 and 109

Results:

Area (probability) = 0.295

b. What weight corresponds with the 6th percentile?

The score you have entered means that the hippo is at the sixth percentile – their percentile rank is 6%

Given P(xZ = -1.555

The value of the z-score tells you how many standard deviations you are away from the mean.

`\begin{gathered} z=(x-\mu)/(\sigma) \\ x=z\sigma+\mu \\ x=-1.555\cdot13+84 \\ x=63.785 \end{gathered}`

63.785 is the weight for the 6th percentile

c. What percentages of hippos are born weighing 27 pounds or less?

Z = (27 - 84)/13

Z-score = -4.38462

0% of hippos are born at 27 pounds or less