Question

Everyday Jo practices her tennis serve by continually serving until she has had a total of 50 successful serves.

Answer 1

Answer:

To reach her goal in the first 100 serves she has to have 50 successful services. This happens with a probability of 2%.

That means she has 98% chances of needing more than 100 serves to reach her goal.

Step-by-step explanation:

The condition for Jo to need more than 100 serves is that she do not accomplish 50 successful serves in 100 tries.

We have a probability sample of possible results that hass a binomial distribution, with n=100 and p=0.4.

As n is large enough, we will approximate it with a normal distribution. The parameters of the normal distribution are:

$\mu=np=100\cdot0.4=40\\\\\sigma=\sqrt{np(1-p)}=\sqrt{100\cdot0.4\cdot0.6}=\sqrt{24}=4.9$

We need the to calculate the probability that the amount of successful services is less than 50, so that she needs more than 100 serves. This is:

$P(X$

We calculate the z value for X:

$z=(X-\mu)/\sigma=(50-40)/4.9=2.04$

Then we have

$P(X$

That means that there is 98% probability that she will need more than 100 serves to reach her goal.