Given a normal distribution with (mean) μ= 50 and (standard deviation) σ = 4, what is the probability that:. a) x>43
b) x<42
c) x>57.5
d) 42 e) x<40 or x>55
f) 5% of the values are less than what X value?
g) 60% of the values are between what two X values (symmetrically distributed around the mean)?
h) 85% of the values will be above what X value?

a) P(x > 43) = 0.9599

b) P(x < 42) = 0.0228

c) P(x > 57.5) = 0.03

d) P(x = 42) = 0.

e) P(x<40 or x>55) = 0.1118

f) 43.42

g) Between 46.64 and 53.36.

h) Above 45.852.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

a) x>43

This is 1 subtracted by the pvalue of Z when X = 43. So

has a pvalue of 0.0401

1 - 0.0401 = 0.9599

P(x > 43) = 0.9599

b) x<42

This is the pvalue of Z when X = 42.

has a pvalue of 0.0228

P(x < 42) = 0.0228

c) x>57.5

This is 1 subtracted by the pvalue of Z when X = 57.5. So

has a pvalue of 0.97

1 - 0.97 = 0.03

P(x > 57.5) = 0.03

d) P(x = 42)

In the normal distribution, the probability of an exact value is 0. So

P(x = 42) = 0.

e) x<40 or x>55

x < 40 is the pvalue of Z when X = 40. So

has a pvalue of 0.0062

x > 55 is 1 subtracted by the pvalue of Z when X = 55. So

has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.0062 + 0.1056 = 0.1118

P(x<40 or x>55) = 0.1118

f) 5% of the values are less than what X value?

X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

43.42 is the answer.

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84.

Between 46.64 and 53.36.

h) 85% of the values will be above what X value?

Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

Above 45.852.

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step-by-step explanation:

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.