# Math Help - Probabilty w/normal distribution

1. ## Probabilty w/normal distribution

Hello all,
I need some help. Here's the info:

A Board of trustees has allocated $400,000 for new beds in three hospital wards. ----------------Obstetrics Surgery Pediatrics Mean # of beds used per day: 24______13__________19 Std. Deviation: 6.1_________4.3_________4.7 Present Capacity: 30________20________24 Cost of adding 1 bed:$20,000 $26,000$15,500

It is possible for a ward to exceed its capacity, but, according to state guidelines, this should not occur more than 5% of the time.

I need to find
1)The probabilty that the demand for beds exceeds capacity in obstetrics.
and
2)I need to answer the following questions:
How many beds should be available in each of the wards?(given the state guidelines)
Has enough money been set aside to achieve this?
How much money is required to add the beds necessary to be in compliance with the state?

Also, if someone can explain what i need to use on a TI-83 calculator to solve this I would be very greatful.

Sorry about the weird looking data table I couldn't get it to fit right.(I attached a copy in Word if it can't be deciphered)

Thanks

2. Originally Posted by mrtimex
Hello all,
I need some help. Here's the info:

A Board of trustees has allocated $400,000 for new beds in three hospital wards. ----------------Obstetrics Surgery Pediatrics Mean # of beds used per day: 24______13__________19 Std. Deviation: 6.1_________4.3_________4.7 Present Capacity: 30________20________24 Cost of adding 1 bed:$20,000 $26,000$15,500

It is possible for a ward to exceed its capacity, but, according to state guidelines, this should not occur more than 5% of the time.

I need to find
1)The probabilty that the demand for beds exceeds capacity in obstetrics.
First you need to know the z score corresponding to demand exceeding supply.

As the normal distribution is continuous we will take this to correspond to 30.5
patients or more. Then:

z=(30.5-24)/6.1=1.065

Now you have to look this up in a table of the cumulative normal distribution.

RonL

3. Originally Posted by mrtimex
Hello all,
I need some help. Here's the info:

A Board of trustees has allocated $400,000 for new beds in three hospital wards. ----------------Obstetrics Surgery Pediatrics Mean # of beds used per day: 24______13__________19 Std. Deviation: 6.1_________4.3_________4.7 Present Capacity: 30________20________24 Cost of adding 1 bed:$20,000 $26,000$15,500

It is possible for a ward to exceed its capacity, but, according to state guidelines, this should not occur more than 5% of the time.

I need to find
1)The probabilty that the demand for beds exceeds capacity in obstetrics.
and
2)I need to answer the following questions:
How many beds should be available in each of the wards?(given the state guidelines)
The z-score that is exceeded 5% of the time for a normal distribution is: 1.645.

Now you need to find the bed capacity that corresponds to this z-score and then round it up to the next integer for each of the wards.

RonL