Statistics math problem standard deviation Best answer 10points!?

Assume that the number of calories in a McDonald’s Egg McMuffin is a normally distributed random variable with a mean of 290 calories and a standard deviation of 14 calories.





(a)What is the probability that a particular serving contains fewer than 300 calories?





(b)More than 250 calories?





(c)Between 275 and 310 calories?





Explain your answer clearly.

Statistics math problem standard deviation Best answer 10points!?
a)


mean=290


sd=14


Find the z-score for each question as z=(x-mean)/sd


p( x %26gt; 300)= p( z %26gt; (300-290)/14) = p( z %26gt; 0.7143)=0.2389





b)p( x %26gt; 250)=p( z %26gt; (250-290)/14) = p( z %26gt; -40/14)=


p(z %26gt; -2.86) = 0.9979





c)p( 275 %26lt; x %26lt; 310) =


z1=(275-290)/14=-1.0714


z2=(300-290)/14=0.7143


p( -1.0714 %26lt; z %26lt; 0.7143) = 0.3577+0.2611=0.6185