1 The weather forecast says there is a 40 chance probability

1) The weather forecast says there is a 40% chance (probability) of rain today and 30% chance of rain tomorrow.
   a)What is the chance of rain on both days? (12%)
   b)What is the chance of rain on neither day? (42%)
   c)What is the chance of rain on at least one day? (58%)

2) Suppose that Y is a normally distributed random variable with ? = 10 and ? = 2, and X is an independent random variable, also normally distributed with ? = 5 and ? = 5. Find:
   a)P(Y>12 and X>4) (0.088 = 8.8%)

b)P(Y>12 or X>4) (0.71 = 71%)

c)P(Y>10 and X<5) (0.25 = 25%)

3) A psychologist is interested in the IQ

Solution

the chance of rain on both days =P(rain for today) P(rain for tomorrow)

0.40(0.30)

=0.12 or 12%

As they are indepdent we multiply the prob

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the chance of rain on neither day = (1-0.4)(1-0.3)

0.42 = 42%

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the chance of rain on at least one day = P(A)+P(B)-P(AB)

= 0.3+0.4-0.12 = 0.58 or 58%

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3)

Stem and leaf plot:

This cannot be said to conform to normal distribution.

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4a) Mean =38.8

std dev =11.696

normal curve with mean 38.8 and std dev 11.696

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6a) Mean = 25.1

std dev = 8.258

NOrmal curve is with mean in the middle 25.1 and std dev = 8.258

For Z value with 70% prob = 0.525

X value = 25.1+0.525(8.258)

= 29.435