Sasha Shasha
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When Moses makes a phone call, the amount of time that the call takes has a normal distribution with
mean 6.5 minutes and standard deviation 1.76 minutes.
(i) 90% of Moses’s phone calls take longer than t minutes. Find the value of t. [3]
z score is 1.282 but how they know whether its - or + ?
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mqb2766
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(Original post by Sasha Shasha)
When Moses makes a phone call, the amount of time that the call takes has a normal distribution with
mean 6.5 minutes and standard deviation 1.76 minutes.
(i) 90% of Moses’s phone calls take longer than t minutes. Find the value of t. [3]
z score is 1.282 but how they know whether its - or + ?
Just @sketch it. If 90% are greater than t, t must be less than the mean so the z score is ...
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RDKGames
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(Original post by Sasha Shasha)
When Moses makes a phone call, the amount of time that the call takes has a normal distribution with
mean 6.5 minutes and standard deviation 1.76 minutes.
(i) 90% of Moses’s phone calls take longer than t minutes. Find the value of t. [3]
z score is 1.282 but how they know whether its - or + ?
The probability in question is P(T>t) = 0.9. The diagram for this is below.

The transformation into the z variable is given by Z = \dfrac{T-\mu}{\sigma}. Hence, the small z value would be z=\dfrac{t-6.5}{1.76}. Since t is less than 6.5, will the difference t-6.5 be +ve or -ve??


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Sasha Shasha
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Thank You
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Sasha Shasha
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(ii) Find the probability that, in a random sample of 9 phone calls made by Moses, more than 7 take

a time which is within 1 standard deviation of the mean.
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RDKGames
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(Original post by Sasha Shasha)
(ii) Find the probability that, in a random sample of 9 phone calls made by Moses, more than 7 take

a time which is within 1 standard deviation of the mean.
Here you've got to take into account that youre looking at a sample of 9 phone calls. So what is the distribution now for T??

If we are interested in calls within 1 standard deviation, then we seek P(\mu-\sigma < T < \mu + \sigma)
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Sasha Shasha
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Can you explain me further on that , im still confused

Thank you
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RDKGames
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(Original post by Sasha Shasha)
Can you explain me further on that , im still confused

Thank you
Well, have you covered the theory on normal distribution regarding samples? If we have a normally distributed population with some mean and standard deviation, and then we take some sample of this population, then the sample will also follow normal distribution with the same mean however its standard deviation will be slightly different.

Are you aware of this, and how the sd must be slightly different ??
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Sasha Shasha
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Nop , can you explain me further ?
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