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

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:

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.

and

The first equation becomes:

Now, simplifying 2nd equation and putting this in:

Now finding mu:

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

The parameters of a normal distribution are the mean and the standard deviation.

From the question, we have:

The 5% of babies means that, the p-value is:

and

The z score at is:

Using z formula, we have:

This gives:

Cross multiply

Make the mean the subject

Also:

The 75% of babies means that, the p-value is:

and

The z score at is:

Recall that:

This gives:

Substitute

Cross multiply

Collect like terms

Divide both sides by 2.31

Substitute in

Hence, the parameter is (12.132, 1.300)

Read more about normal distribution at:

link

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step-by-step explanation:

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step-by-step explanation: