Question

while only 5% of babies have learned to walk by the age of 10 months, 75% are walking by 13 months. if the age at which babies develop the ability to walk can be described by a normal model, find the parameters

Answer 1

Answer:

$mu=12.1299$

$\sigma=1.2987$

Step-by-step explanation:

In the normal distribution curve, we will have 5% below 10 months [horizontal axis] and 75% below 13 months [horizontal axis].

We need to find z-score using z-table [normal table] that corresponds to

5% = 0.05

and

75% = 0.75

Zscore formula:

$z=\frac{x-\mu}{\sigma}$

Where mu is mean and sigma is standard deviation [these are the 2 parameters we are seeking]

So, 0.05 corresponds to z = -1.64, and

0.75 corresponds to z = 0.67

Now we put both of these into z-score formula and solve both equations for mu and sigma.

$-1.64=\frac{10-\mu}{\sigma}$

and

$0.67=\frac{13-\mu}{\sigma}$

The first equation becomes:

$-1.64=\frac{10-\mu}{\sigma}\\-1.64\sigma+\mu=10\\mu=10+1.64\sigma$

Now, simplifying 2nd equation and putting this in:

$0.67=\frac{13-\mu}{\sigma}\\0.67\sigma=13-(10+1.64\sigma)\\0.67\sigma=13-10-1.64\sigma\\2.31\sigma=3\\\sigma=1.2987$

Now finding mu:

$\mu=10+1.64(1.2987)\\\mu=12.1299$

These two MU(mean) and SIGMA(standard deviation) are the 2 parameters.