Question

Measurements were recorded for the slapshot speed of 100 minor-league hockey players. These measurements were found to be normally distributed with mean of 81.417 mph and standard deviation of 1.1983 mph. Would it be unusual to record a value between 81.2 and 81.43 mph?

Question 5 options:

1)	A value in this interval is not unusual.

2)	A value in this interval is borderline unusual.

3)	A value in this interval is unusual.

4)	We do not have enough information to determine if a value in this interval is unusual.

5)	It is impossible for a value in this interval to occur with this distribution of data.

A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $107.118 million with a standard deviation of $13.1377 million. Given this information, 87.18% of movies grossed greater than how much money (in millions)? Assume the distribution is approximately normal.

Question 3 options:

1)

122.03

2)	We do not have enough information to calculate the value.

3)

303.01

4)

92.21

5)

88.77

The daily stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when adjusting for inflation) with a mean of $131.048 and standard deviation of $2.7756 Approximately 9.44% of days IBM had a stock price greater than what dollar amount?

Question 4 options:

1)

134.7

2)

127.4

3)

120.92

4)

141.17

5)	We do not have enough information to calculate the value.

Answer 1

1)

When the value is with in two standard deviations then it is not unusal

Here mean = 81.417

S.d = 1.1983

So, 81.417 - (2*1.1983), 81.417 + (2*1.1983)

(79, 84)

So the given interval (81.2, 81.43) is inside these values

So, the value in the given interval is not unusual

2)

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 107.118

S.d = 13.1377

From z table, P(z>-1.13) = 0.8718

So, -1.13 = (x - 107.118)/13.1377

X = 92.27

Closest answer is 92.21

3)

Mean = 131.048

S.d = 2.7756

From z table, P(z>1.31) = 0.0944

1.31 = (x - 131.048)/2.7756

X = 134.7