Question

Can you help me with this problem, thanks
Weights of male mountain lions follow the normal distribution with a median of 150 lb and an interquartile range of 8.2 lb.

1. Find the 75th percentile of the weights.

2. Find the 95th percentile of the weights.

Answer 1

Explanation way forward-a)
The standard deviation can be calculated using the formula
σ=Interquartile range/1.34896=upperquartile -lowerquartile=8.2lb/1.34896
For this case the standard deviation is 8.2/1.34896= 6.079
A standard normal distribution table shows the z-score for a cumulative probability of 75% is z = 0.675 The median and the mean are the same. Therefore the following formula can be used: z=X−μσ Substituting we get 0.675=X−1506.079 Solving for X gives
X = 150 + 4.1= finish yourselef the rest and plot the box plot see ghrafically
explanation way forward b) A standard normal distribution table shows the z-score for a cumulative probability of 95% is z = 1.645
The median and the mean are the same. Therefore the following formula can be used:
z=X−μσ

Substituting we get
1.645=X−1506.079

X=150+(1.645×6.079)=finish yourself

then do it the Box plot so you see graphically better