Mumuni Bawumia, a farmer sells 500 litres of fresh milk a day with a standard deviation of 35 litres. Given that the daily sales of fresh milk is normally distributed, what is the probability that the sales in any single day is: a. Greater than 506 litres

b. Between 498 litres and 506 litres.
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a:     0.43194

b:     0.09084

Step-by-step explanation:

First construct the z values for 498 and 506.

=-0.05714

z(506)=(506-500)/35=0.17143

Check the cumulative normal distribution tables to find

P(x<=-0.05714)=0.47722

P(x<=506)=0.52278

These probabilities imply that

P(x>506)=1-P(x<=506)=1-0.52278=0.43194

P(498<=x<=506)=P(x<=506)-P(x<=498)=0.09084

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40