Answer:
12 years younger.
Step-by-step explanation:
Let Jan's age be J and Karyn's age be K.
![J= \frac{2}{3} K](https://tex.z-dn.net/?f=J%3D%20%5Cfrac%7B2%7D%7B3%7D%20%20K)
Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.
![J-8 = \frac{2}{5} (K+4)](https://tex.z-dn.net/?f=J-8%20%3D%20%5Cfrac%7B2%7D%7B5%7D%20%28K%2B4%29)
=> ![(\frac{2}{3} - \frac{2}{5} ) K = \frac{8}{5} + 8](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B3%7D%20-%20%5Cfrac%7B2%7D%7B5%7D%20%29%20K%20%3D%20%5Cfrac%7B8%7D%7B5%7D%20%2B%208)
=> 4K = 48 X 3
=> K= 36.
=> J= 24.
So Jan is 12 years younger.
All the equivalent fractions.
I'm fairly certain that's correct but check again if you need to and please, correct me if I got something wrong.
Answer:
a: 0.9544 9 within 8 units)
b: 0.9940
Step-by-step explanation:
We have µ = 300 and σ = 40. The sample size, n = 100.
For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:
P(292 < x < 308).
We need to find the z-scores that correspond to these values using the given data. See attached photo 1 for the calculation of these scores.
We have P(292 < x < 308) = 0.9544
Next we want the probability of the sample mean to be within 11 units of the population mean, so we want the values from 289 to 311. We want to find
P(289 < x < 311)
We need to find the z-scores that correspond to these values. See photo 2 for the calculation of these scores.
We have P(289 < x < 311) = 0.9940