Question

Can you help me with this problem?
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

The standard deviation can be calculated using the formula
σ=Interquartile range/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

Can you do the next one?

Answer 2

Apply my formula and get the answer to the 2nd question, I cannot give you the full answer else I may be reported.

Answer 3

It's the formula.

Answer 4

Mhm.

Answer 5

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:
\[z=\frac{X-\mu}{\sigma}\]
Substituting we get
\[1.645=\frac{X-150}{6.079}\]
\[X=150+(1.645\times 6.079)=you\ can\ finish\]

Answer 6

@Dharmaputra_993 Note the mistakes in your reproduction of the solution to 1.

Answer 7

Didn't see those before, sorry and thanks!