A plant biologist studies the height of sunflowers. He measures a large sample of sunflowers and creates a probability distribution. The distribution is normal in shape with mean 112 cm and standard deviation 16 cm. What is the probability (approximately) that a sunflower will be less than 136 cm tall?

Probability that a sunflower will be less than 136 cm tall is 0.9332.

Step-by-step explanation:

We are given that a plant biologist studies the height of sunflowers. He measures a large sample of sunflowers and creates a probability distribution.

The distribution is normal in shape with mean 112 cm and standard deviation 16 cm.

Let X = height of sunflowers

So, X ~ N()

The z-score probability distribution for single selected value is given by;

                Z =  ~ N(0,1)

where, = population mean height = 112 cm

             = standard deviation = 16 cm

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that a sunflower will be less than 136 cm tall is given by = P(X < 136 cm)

    P(X < 136 cm) = P( < ) = P(Z < 1.50) = 0.9332

The above probabilities is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

Hence, probability that a sunflower will be less than 136 cm tall is 0.9332.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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the answer is d

step-by-step explanation: