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Express Lane Plus
Posts: 363
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5 months ago
The average time spent sleeping​ (in hours) for a group of medical residents at a hospital can be approximated by a normal​ distribution, as shown in the graph to the right. Answer parts​ (a) and​ (b) below.
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wrote...
Staff Member
5 months ago
a)
1.645 = (X - 6.1)/1
X = 1.645 + 6.1
X = 7.745 or 7.75 on rounding to 2 dps
Shortest sleeping time that place a resident in the top 5% of is 7.75 hours


b)Between what two values does the middle 50% of the sleep times lie?


The z values concerned are - 0.675 and + 0.675
- 0.675 = (X - 6.1)/1
X = 6.1 - 0.675
X = 5.425

or 5.43+ 0.675 = (X - 6.1)/1
X = 6.1 + 0.675
X = 6.775 or 6.78
Middle 50% sleep times lie between 5.43 hours and 6.78 hours
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wrote...
Express Lane Plus
5 months ago
a) 1.645 = (X - 6.1)/1 X = 1.645 + 6.1 X = 7.745 or 7.75 on rounding to 2 dps Shortest sleeping time that place a resident in the top 5% of is 7.75 hours b)Between what two values does the middle 50% of the sleep times lie? The z values concerned are - 0.675 and + 0.675 - 0.675 = (X - 6.1)/1 X = 6.1 - 0.675 X = 5.425 or 5.43+ 0.675 = (X - 6.1)/1 X = 6.1 + 0.675 X = 6.775 or 6.78 Middle 50% sleep times lie between 5.43 hours and 6.78 hours
it was incorrect !!!!!!
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wrote...
Educator
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Posts: 24524
5 months ago Edited: 5 months ago, bio_man
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a) 1.645 = (X - 6.1)/1 X = 1.645 + 6.1 X = 7.745 or 7.75 on rounding to 2 dps Shortest sleeping time that place a resident in the top 5% of is 7.75 hours

I'm not certain if "TOP 5" means 0.95 = z or 0.05 = z, that is, if they want the 95th percentile OR 5th percentile.

This will give you different answers. I'm assuming they want the 95th percentile, so choose the larger of the 2, 7.64.

You haven't uploaded question (b).

Please upload it when you get a chance, and I'll be around to answer more questions over the weeked Smiling Face with Open Mouth

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wrote...
Educator
5 months ago
b)Between what two values does the middle 50% of the sleep times lie?

Where did you find this question?
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