Which Rust RNG should be used for multithreaded sampling?

I am trying to create a function in Rust which will sample from M normal distributions N times. I have the sequential version below, which runs fine. I am trying to parallelize it using Rayon, but am encountering the error

Rc<UnsafeCell<ReseedingRng<rand_chacha::chacha::ChaCha12Core, OsRng>>> cannot be sent between threads safely

It seems my rand::thread_rng does not implement the traits Send and Sync. I tried using StdRng and OsRng which both do, to no avail because then I get errors that the variables pred and rng cannot be borrowed as mutable because they are captured in a Fn closure.

This is the working code below. It errors when I change the first into_iter() to into_par_iter().

use rand_distr::{Normal, Distribution};
use std::time::Instant;
use rayon::prelude::*;

fn rprednorm(n: i32, means: Vec<f64>, sds: Vec<f64>) -> Vec<Vec<f64>> {

    let mut rng = rand::thread_rng();
    let mut preds = vec![vec![0.0; n as usize]; means.len()];

    (0..means.len()).into_iter().for_each(|i| {
        (0..n).into_iter().for_each(|j| {
            let normal = Normal::new(means[i], sds[i]).unwrap();
            preds[i][j as usize] = normal.sample(&mut rng);
        })
    });

    preds
}

fn main() {

    let means = vec![0.0; 67000];
    let sds = vec![1.0; 67000];
    let start = Instant::now();
    let preds = rprednorm(100, means, sds);
    let duration = start.elapsed();
    
    println!("{:?}", duration);
}

Any advice on how to make these two iterators parallel?

Thanks.